The ABC of Structured Products

© Incisive Media Investments Limited, 2005.

All rights reserved.No part of this publication may be reproduced, stored in or introduced into any retrieval system, or transmitted, in any form or by any means,electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright owners.

Asia Risk and Société Générale (“SG”) and Lyxor Asset Management (“Lyxor”) have made every effort to ensure the accuracy of the text.However, neither it nor any company associated with the publication can accept legal or financial responsibility for the consequences thatmay arise from errors, omission or any opinions given.

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The information contained in this document is provided for general educational and informational purposes only. It should not be treated as a substitute for professional advice in relation to any matters contained herein. Changes in circumstances and market practice may occur after the compilation of this document which may make the information contained herein no longer accurate or different from thecurrent position. While the information herein is derived from sources reasonably believed to be reliable, SG, Lyxor and their affiliates do not represent or warrant the reliability, accuracy, completeness, timeliness or fitness for any purpose of any of the information.You should not rely upon any information contained in this document for any transaction or purpose. You should consult your own legal,financial, investment, tax and other professional advisors, where appropriate. As none of SG, Lyxor and their affiliates intend to give anyadvice in this document, SG, Lyxor and their affiliates cannot and will not be responsible for any loss resulting from your relying on any of theinformation contained in this document. Nothing herein shall constitute an offer, a solicitation for an offer, or an invitation, advertisement,inducement, advice or recommendation to buy or sell, or to otherwise transact, any securities, derivatives, treasury products and structuredfinancial products.

2 The ABC of Structured Products

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www.asiarisk.com.hk

Welcome to the Asia Risk/Société Générale glossary for structured

products, an invaluable guide for structurers, traders, marketers,

distributors, analysts, journalists and investors in this fast-growing market.

However complicated they may seem to the investor, today’s

structured products are based around a combination of some very basic

financial concepts.This book brings these concepts together and offers

standardised definitions and explanations, which can be understood by

the layman and PhD quant alike. It also explains some of the more

common combinations of these essential financial building blocks, while

allowing the imaginations of structurers to roam freely through the terms

dreaming up new and profitable structures.

Terms were selected by the team at Société Générale, with additional

research by Asia Risk journalists.We searched all available literature, spoke

to hundreds of traders and used SG trading and structuring expertise to

select the most common, yet often most misunderstood, words and

phrases.Terms were selected for their fundamental importance and

common use – alas, we had to reject the hamster option, which despite

the clever pun on the German for “range accrual”, has never been heard on

an Asian trading floor nor structurers’office. But we have nearly 500 terms,

representing the most complete guide to structured products

terminology in the market today.

Foreword

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US & Canada Office IncisiveMedia Plc,270 Lafayette Street, Suite 700,New York, NY 10012, USATel (212) 925 6990;fax (212) 925 7585

The ABC of Structured Products

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T he Asian structured products market hasboomed over the past few years.Starting in 1999, when the first capital-

guaranteed funds were launched in HongKong, these products have become a hit withinvestors due to their higher potential returnsthan bank deposits. In early 2002, there were73 guaranteed funds authorised for sale by theSecurities and Futures Commission in HongKong with a net asset value (NAV) of US$11.7billion. The number has surged to more than300 guaranteed funds worth more than US$18billion in NAV at the time of writing.

But these figures are only the tip of theiceberg, as they only include funds authorisedfor sale to the public. They do not include thehuge volumes of structured notes and productof ferings in the private banking andinstitutional markets, where growth has beeneven more tremendous. The Asian market nowrivals (some would argue leads) the Europeanand US markets in terms of sophistication, witha huge variety of exotic structures available toprivate banking clients.

Over the past two years, retail investors havealso become much more knowledgeable aboutstructured products, and an improved equityoutlook means investors are no longer satisfiedwith simple guaranteed funds. The low interestrate environment led investors to take hugeinterest in products that enabled them to sellvolatility for yields. Since 2003, the market hasseen a proliferation of structures, such as target

redemption notes (Tarns), equity-linked notes,range accruals and accumulator notes.

Investors have also become moredemanding. The first Tarns typically had a 10-year maturity, and most of the structures aimedat retail investors were 100% principalprotected. But non-principal-protectedproducts quickly became a sell-out as investorsstarted to demand shorter tenors, higherpayouts and more innovative features.

The massive amounts of volatility productsthat have been sold across Asia to privatebanking and retail investors contributed to afall in implied volatility levels. Productproviders started to incorporate views oncorrelation into equity-linked notes to increasepayouts. Basket equity-linked notes that payhigh coupons and additional amounts based oneither the best or worst performer in a basket ofstocks are now a staple of the market.

Structured products with Asian underlyingshave also been hugely successful. Lyxor AssetManagement, a 100% subsidiary of the SociétéGénérale Group (SG), recently offered aproduct called Alpha Equity Fund – Hang SengIndex, which incorporates payouts based on aformula that tracks the index over aninvestment cycle of eight years and locks in thehighest positive performance of the index. Atmaturity, if the index is above its initial level,investors will get a return based on the highestpositive performance observed. If the indexfalls below its initial level, investors will get a

Introduction

4 The ABC of Structured Products

History of structured products in Asia

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return based on the performance of the indexplus the highest performance observed.

SG’s expertiseSG CIB, the corporate and investmentbanking arm of SG, is a multi-award-winningleader in structured products, both in Asia andglobally. This position is backed by itsextensive network in more than 45 countriesacross Europe, the Americas and the Asia-Pacific region, and its leading expertise inderivatives across equities, interest rate, credit,foreign exchange and commodities.

In the Asia-Pacific, SG CIB has built primeinvestment banking operations to become aleading regional player in derivatives,structured finance and debt capital markets.We combine global and local strengths toprovide corporate clients, financial institutionsand private investors with value-addedintegrated financial solutions.

SG and its 100% subsidiary Lyxor AssetManagement – which won the Asset Managerof the Year 2004 award from Asia Risk – arealso leading innovators in alternativeinvestments. With a platform of 150 managedaccounts and more than €20 billion of assetsunder management, Lyxor Asset Managementis a recognised expert in hedge fund managerselection. In January 2004, SG launched thefirst capital-guaranteed hedge fund product totarget Hong Kong retail investors, a structurereferenced to the MSCI Hedge Invest Index,which comprises managed accounts on theLyxor platform. More recently, Lyxor AssetManagement launched Hong Kong’s firstretail-guaranteed product linked to real estateinvestment trusts.

Hong Kong is SG’s structured financeregional hub, providing leading capabilities inproject finance, export finance, syndication,debt capital markets and credit derivatives. The

territory is also the major centre for SG’s equityderivatives business with market-leadingwarrants and structured products. SG alsoprovides worldwide expertise ranging fromequity advisory and mergers and acquisition toprivate banking, asset management and futures.

Need for education In the structured products world, words suchas ‘Everest’ and ‘Parisian’ have very differentmeanings from their common daily usage. Thegrowing complexity of products means thatmany new options and structures are constantlybeing created and new terminology devisedand added to the universe of product jargon.Keeping up with the latest trends in structuredproducts means learning the language andunderstanding how the options work.Understanding a product also meansunderstanding the risks behind it. While mostinvestors have fairly good product knowledge,there are still certain misperceptions aboutproduct risks. For example, many perceive a‘guaranteed’ product to be risk-free. In reality,a guarantee on principal repayment is subject tocredit risk of the guarantor and usually holdsonly when the product is held to maturity.

This glossary is an A to Z guide to helpreaders navigate the maze of structuredproduct terms. The focus here is on equityderivatives, but many of the options andfeatures have been adapted to products of otherasset classes. With this guide in hand, investorswill find that the structured products languageis not as daunting as it may first have seemed. ●

Introduction

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www.asiarisk.com.hk

ContactSGNicolas Reille, Managing Director Structured Products Asia EX Japan Tel: +852 2166 4918 Email: [email protected]


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Glossary of terms

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AAccretingA description, applicable to a variety ofinstruments, denoting that the notionalprincipal increases successively over thelife of the instrument, eg, caps, collars,swaps and swaptions. If the increase takesplace in increments, the instrument maybe known as a step-up. See also amortising

Accrual corridorThe range within which an underlyingreference rate must trade for couponpayments to accrue in a range note orcorridor option.

Accrual noteSee range note

Accrual periodPeriod over which net payment or receiptpertaining to swaps is accrued. It isinclusive of the start date and runs to theend date without including the end date.

All-or-nothing option See binary option

AlphaAlpha is used to measure theperformance of a fund in relation to itsbenchmark. An alpha that measures 2.0indicates a fund has achieved a return 2%better than could have been expectedfrom its benchmark.

Alternative risk transferAn approach to risk managementcombining capital markets, reinsurance

and investment banking techniques thatallows a party to either free itself fromrisks not easily transferred via traditionalinsurance, or alternatively cover such risksin a non-traditional way – by using thecapital markets for example.

AltiplanoAn Altiplano is a type of mountain rangestructure, which offers investors a fixedpayout at the end of the product’s life on the condition that none of theassets that make up the underlyingbasket have decreased below a givenlevel. If the level is breached, the productpays a capital guarantee plusparticipation in the growth of the totalunderlying basket.

American-style option The holder of an American-style optionhas the right to exercise the option at anytime during the life of the option, up toand including the expiry date. See alsooption styles

Amortising A description, applicable to a variety ofinstruments, denoting that the notional principal decreases successivelyover the life of an instrument, eg,amortising swap, index amortising rateswap, amortising cap, amortising collar,amortising swaption. If the decrease takes place in increments, the instrumentmay be known as a step-down.Mortgage-style amortisation refers to anamortising swap such that the principal


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amortisation plus interest is the same amount in each interest period.See also accreting

AnnapurnaAn Annapurna is a kind of mountainrange product, which offers a returnequal to the greater of a capitalguarantee plus a fixed coupon and aparticipation in the performance of theunderlying basket.The level of the fixedcoupon and of the participation rate inthe performance depend on if and whenthe worst-performing stock breaches adownside barrier.The later the breach, thehigher the fixed coupon and equityparticipation rate.

Annuity swap An interest rate swap in which a series ofirregular cashflows are exchanged for astream of regular cashflows of equivalentpresent value.

ArbitrageA guaranteed or riskless profit fromsimultaneously buying and sellinginstruments that are perfect equivalents, the first being cheaper than the second.

Arbitrage-free modelAny model that does not allow arbitrageon the underlying variable. Some simpleearly models assumed parallel shifts inthe yield curve, but the varying yields ofdifferent duration bonds could bearbitraged using butterfly strategies.

AutoRegressive conditionalheteroscedasticity (Arch) A discrete time model for a randomvariable. It assumes that variance isstochastic and is a function of thevariance of previous time steps and thelevel of the underlying.

Asian optionSee average option

Asset allocationThe distribution of investment fundswithin a single asset class or across anumber of asset classes (such as equities,bonds and commodities) with the aim ofdiversifying risk or adding value to aportfolio. See also overlay

Asset backed securityAn asset backed security is a securitycollateralised by assets such as bonds,credit card repayments, loan repaymentsor real estate.

Asset swap A package of a cash credit instrumentand a corresponding swap thattransforms the cash flows of the non-parinstrument (bond or loan), into a par(floating interest rate) structure.Asset swaps typically transform fixed-rate bonds into par floaters,bearing a net coupon of Libor plus aspread, although cross-currency asset swaps, transforming cashflows from one currency to another are also common.


Glossary of terms

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AAsset/liability managementThe practice of matching the termstructure and cashflows of anorganisation’s asset and liability portfoliosin order to maximise returns andminimise risk. An institutional example ofthis would be a bank converting a fixed-rate loan (asset) by utilising a fixed-for-floating interest rate swap to match itsfloating rate funding (deposits).

At-the-money 11.. At-the-money forward: An optionwhose strike is set at the same level as theprevailing market price of the underlyingforward contract.With a Black-Scholesmodel, the delta of a European-style, at-the-money forward option will be closeto 50%.22.. At-the-money spot: An option whosestrike is set the same as the prevailingmarket price of the underlying. Becauseforwards commonly trade at a premiumor discount to the spot, the delta may notbe close to 50%. See also in-the-money, out-of-the-money

AutocapA standard cap consists of a series ofcaplets hedging future floating ratepayments. However, autocaps onlyprovide a hedge for the first pre-specifiednumber of in-the-money caplets afterwhich the option expires, and so are acheaper alternative to caps.

Average optionA plain vanilla option pays out the

difference between its predeterminedstrike price and the spot rate (or price) ofthe underlying at the time of expiry.Thepurchaser of an average option (averageprice, average strike, average hybrid,average ratio), on the other hand, willreceive a pay-out which depends on theaverage value of the underlying.Theaverage can be calculated in a number ofways (arithmetic or geometric, weightedor simple) from the spot rate on apredetermined series of dates. An averagerate (or average price) option is a cash-settled option with a predetermined (iefixed) strike which is exercised at expiryagainst the average value of theunderlying over the specified dates. Ingeneral, hedging with an average optionis cheaper than using a portfolio of vanillaoptions, since the averaging processoffsets high values with low ones andtherefore lowers volatility and premium.Average options, also known as Asianoptions, are particularly popular in theequity, currency and commodity markets.In contrast, the strike for an average strikeoption is not fixed until the end of theaveraging period which is typically muchbefore the expiry.When the strike is set,the option is exercised against theprevailing spot rate. Unlike average priceoptions, average strike options may beeither cash or physically settled. In the caseof an average hybrid option (also knownas an average-in/average-out option), boththe strike and settlement price of theoption are determined using the average,where the strike averaging period typically




Glossary of terms

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precedes the settlement price averagingperiod. For the average ratio option, boththe strike and settlement price of theoption are determined using the averageas in the hybrid case.The final payout isdetermined by comparing the ratio ofsettlement price to strike and a fixedpercent strike.

Average price optionSee average option

Average rate optionSee average option

Average strike optionSee average option

BBack-testingThe validation of a model by feeding ithistorical data and comparing themodel’s results with the historical reality.The reliability of this technique generallyincreases with the amount of historicaldata used.

Barrier optionBarrier options, also known as knock-out,knock-in or trigger options, are path-dependent options which are eitheractivated (knocked-in) or terminated(knocked-out) if a specified spot ratereaches a specified trigger level (or levels)between inception and expiry. Before

termination knock-out options behaveidentically to standard European-styleoptions, but carry lower initial premiumsbecause they may be extinguished beforereaching maturity. In contrast, knock-inoptions behave identically to European-style options only if they are activated/knocked-in and so also command a lower premium.

The standard barrier options havebarrier levels that are monitoredcontinually during the lifetime of theoption. Single barrier options that have abarrier level above current spot areclassified as up-and-out or up-and-inoptions. For single barriers below spot theusual terminology is down-and-out forthe knock-out barrier option, and down-and-in for the knock-in barrier option.

Many variations on the barrier themeare available. Barrier levels can bemonitored continually, at discrete fixingtimes (discrete barrier options) or only atthe final expiry date of the option (at-expiry barrier options). Barriers may beactive only during distinct time intervals(window barrier options) or may changevalue at fixed points during the lifetime ofthe option (stepped barrier options).Barriers may need to be breached for acertain time before they are consideredtriggered (Parisian Barrier Options) or mayallow for partial triggering dependingupon how far beyond the trigger level theunderlying asset is observed (Soft Barrieroptions). Barriers may reference a differentunderlying to that of the option itself –such barriers are known as outside


Glossary of terms

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Bbarriers. See also discrete barrier option,double barrier option, Parisian barrieroption, path-dependent option, trigger,trigger condition

Basis 11.. The difference between the price of afutures contract and its theoretical value.22.. The convention for calculating interestrates. A bond can be 30/360 or actual/365in the US, or 360/360 in Europe. Moneymarket instruments can be actual/360 inthe US or actual/365 in the UK and Japan.

Basis risk In a futures market, the basis risk is the riskthat the value of a futures contract doesnot move in line with the underlyingexposure. Because a futures contract is aforward agreement, many factors canaffect the basis.These include shifts in theyield curve, which affect the cost of carry;a change in the cheapest-to-deliver bond;supply and demand; and changingexpectations in the futures market aboutthe market’s direction. Generally, basis riskis the risk of a hedge’s price not moving inline with the price of the hedged position.For example, hedging swap positions withbonds incurs basis risk because changesin the swap spread would result in thehedge being imperfectly correlated. Basisrisk increases the more the instrument tobe hedged and the underlying areimperfect substitutes.

Basis swapAn interest rate basis swap or a cross-

currency basis swap is one in which twostreams of floating rate payments areexchanged. Examples of interest ratebasis swaps include swapping $Liborpayments for floating commercial paper,Prime,Treasury bills, or Constant MaturityTreasury rates; this is also known as afloating-floating swap. A typical cross-currency basis swap exchanges a set ofLibor payments in one currency for a setof Libor payments in another currency.

Basis tradingTo basis trade is to deal simultaneously in a derivative contract, normally a future, and the underlying asset.Thepurpose of such a trade is either to coverderivatives sold, or to attempt anarbitrage strategy.This arbitrage caneither take advantage of an existingmispricing (in cash-and-carry arbitrage) or be based on speculationthat the basis will change. See also cash-and-carry arbitrage

Basket credit default swapA credit default swap which transferscredit risk with respect to multiplereference entities. For each referenceentity, an applicable notional amount isspecified, with the notional of the basketswap equal to the aggregate of thespecified applicable notional amounts.Types of basket credit default swapsinclude linear basket credit default swaps,first-to-default basket credit defaultswaps, and first-loss basket credit defaultswaps. See also credit default swap




Glossary of terms

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Basket option An option that enables a purchaser tobuy or sell a basket of currencies,equities or bonds.

Basket swapA swap in which a floating leg is based onthe returns on a basket of underlyingassets, such as equities, commodities,bonds, or swaps.The other leg is usually(but not always) a reference interest ratesuch as Libor, plus or minus a spread.

Basket trading See program trading

Bear spreadAn option spread trade that reflects abearish view on the market. It is usuallyunderstood as the purchase of a putspread. See also bull spread, call spread

Bermudan option The holder of a Bermudan option, alsoknown as a mid-Atlantic option, has theright to exercise it on one or morepossible dates prior to its expiry.See also option styles

Best-of optionA best-of option pays out on the bestperforming of a number of underlyingassets over an agreed period of time.For instance, if a basket contains stock A, stock B and stock C and stock Bgains in value by the larger amountduring the products term, then the

payout would be based on the increase invalue of Stock B.

Beta 11.. The beta of an instrument is itsstandardised covariance with its class ofinstruments as a whole.Thus the beta of astock is the extent to which that stockfollows movements in the overall market.22.. Beta trading is used by currencytraders if they take the volatility risk ofone currency in another. For example,rather than hedge a sterling/yen optionwith another sterling/yen option, a trader,either because of liquidity constraints orbecause of lower volatility, might hedgewith euro/yen options.The beta riskindicates the likelihood of the twocurrencies’ volatilities diverging.

Better-of-two-assets option See best-of option

Bilateral nettingAgreement between two counterpartieswhereby the value of all in-the-moneycontracts is offset by the value of all out-of-the money contracts, resulting in a single net exposure amount owed by one counterparty to the other.Bilateral netting can be multi-productand encompass portfolios of swaps,interest rate options, and forward foreign exchange.

Binary optionUnlike simple options, which havecontinuous pay-out profiles, that of a


Glossary of terms

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Bbinary option is discontinuous and paysout a fixed amount if the underlyingsatisfies a predetermined triggercondition but nothing otherwise. Binaryoptions are also known as digital or all-or-nothing options.

There are two major forms: at maturityand one-touch. At maturity binaries, alsoknown as European binaries or at expirybinaries, pay out only if the spot tradesabove (or below) the trigger level atexpiry. One-touch binary options, alsoknown as American binaries, pay out ifthe spot rate trades through the triggerlevel at any time up to and includingexpiry.The pay-out of a one-touch binarymay be due as soon as the triggercondition is satisfied or alternatively atexpiry (one-touch immediate or one-touch deferred binaries). As with barrieroptions, variations on the theme includediscrete binaries, stepped binaries, etc.Binary options are frequently combinedwith other instruments to createstructured products, such as contingentpremium options.

Binomial model Any model that incorporates a binomial tree.

Binomial tree Also called a binomial lattice. A discretetime model for describing the evolutionof a random variable that is permitted torise or fall with given probabilities. Afterthe initial rise, two branches will eachhave two possible outcomes and so the

process will continue.The process isusually specified so that an upwardmovement followed by a downwardmovement results in the same price, sothat the branches recombine. If thebranches do not recombine it is known asa bushy, or exploded, tree.The size of themovements and the probabilities arechosen so that the discrete binomialmodel tends to the normal distributionassumed in option models as the numberof discrete steps is increased. Options canbe evaluated by discounting the terminalpay-off back through the tree using thedetermined probabilities. Interest inbinomial trees arises from their ability todeal with American-style features and toprice interest rate options. For example,American-style options can readily bepriced because the early exercisecondition can be tested at each point inthe tree.

Black-Derman-Toy model A one-factor log-normal interest ratemodel where the single source ofuncertainty is the short-term rate.The inputs into the model are theobserved term structure of spot interest rates and their volatility termstructure.The Black-Derman-Toy model,such as the Ho-Lee model, describes theevolution of the entire term structure in a discrete-time binomial treeframework.The model can be used toprice bonds and interest rate-sensitivesecurities, though the solutions are notclosed-form.




Glossary of terms

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Black-Scholes model The original closed-form solution tooption pricing developed by Fischer Blackand Myron Scholes in 1973. In its simplestform it offers a solution to pricingEuropean-style options on assets withinterim cash pay-outs over the life of theoption.The model calculates thetheoretical, or fair value for the option byconstructing an instantaneously risklesshedge: that is, one whose performance isthe mirror image of the option pay-out.The portfolio of option and hedge canthen be assumed to earn the risk-free rateof return.

Central to the model is the assumptionthat market returns are normallydistributed (ie have lognormal prices),that there are no transaction costs, thatvolatility and interest rates remainconstant throughout the life of theoption, and that the market follows adiffusion process.The model has fivemajor inputs: the risk-free interest rate,the option’s strike price, the price of theunderlying, the option’s maturity, and thevolatility assumed. Since the first four areusually determined by the market,options traders tend to trade the impliedvolatility of the option.

BondCompanies or governments issue bonds as a means of raising capital. Thebond purchaser is in effect making aloan to the issuer, and unlike with sharesinvestors at no point hold a stake in the company.

Bond index swap A swap in which one counterpartyreceives the total rate of return of a bondmarket or segment of a bond market inexchange for paying a money marketrate. Counterparties may also swap thereturns of two bond markets.

Box To buy/sell mispriced options and hedge the market risk using only options,unlike the conversion or the reversal,which use futures contracts. If a certainstrike put is underpriced, the trader buysthe put and sells a call at the same strike,creating a synthetic short futuresposition.To get rid of the market risk, hesells another put and buys another call,but at different strike prices. See alsoconvergence trade

Brace-Gatarek-Musiela (Bgm) model See market model of interest rates.

Bull spreadAn option spread trade that reflects abullish view on the market. It is usuallyunderstood as the purchase of a callspread. See also bear spread, call spread

Butterfly spread The simultaneous sale of a straddle andpurchase of a money strangle.Thestructure profits if the underlying remainsstable, and has limited risk in the event ofa large move in either direction. As atrading strategy to capitalise upon arange trading environment it is usually


Glossary of terms

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B/Cexecuted in equal notional amounts.Alternatively, such trades are oftenapplied to benefit from changes involatility. In such circumstances thebutterfly spread is traded on a ‘vega-neutral’ basis (ie the volatility sensitivityof the long position is initially offset bythe volatility sensitivity of the shortposition). As the holder of an initiallyvega-neutral spread, the trader willbenefit from changes in volatility sincethe strangle position profits more from anincrease in volatility than the straddle andloses less than the straddle in a decline involatility (this is due to the fact that thevomma of the strangle is higher than thatof the straddle).

CCalendar spreadA strategy that involves buying andselling options or futures with the same(strike) price but different maturities. Sucha strategy is used in futures when onecontract month is theoretically cheap andanother is expensive.With options, thestrategy is often used to play the shapeof or expected changes in, the volatilityterm structure. For example, if one-monthvolatility is high and one-year volatilitylow, arbitrageurs might buy one-yearstraddles and sell short-term straddles,thereby selling short-term volatility andbuying long-term volatility. If, all elsebeing equal, short-term volatility declines

relative to long-term volatility, thestrategy makes money.

Call option See option

Call spread A strategy that reduces the cost of buyinga call option by selling another call at ahigher strike price (Bull call spread).Thislimits potential gain if the underlyinggoes up, but the premium received from selling the out-of-the-money call partly finances the at-the-money call. A call spread may be advantageous if the purchaser thinks there is onlylimited upside in the underlying.Alternatively a Bear call spread can beconstructed by selling a call option and buying another at a higher strikeprice. See also bear spread, bull spread, put spread

Callable swap An interest rate swap in which the fixed-rate payer has the right toterminate the swap after a certain time if rates fall. Often done inconjunction with callable debt issueswhere an issuer is more concerned withthe cost of debt than the maturity. Theembedded option is, in effect, a swaptionsold by the fixed-rate receiver whichenables the fixed-rate payer to receivethe same high fixed rate for theremaining years of the swap in the eventthat interest rates fall. The fixed ratereceived under the swaption offsets the




Glossary of terms

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fixed rate paid under the original swapeffectively cancelling the swap. In somedefinitions of a callable swap, the fixed-rate receiver has the right toterminate the swap. Also known as acancellable swap.

Cancellable swap See callable swap

Cap A contract whereby the seller agrees topay to the purchaser, in return for anupfront premium or a series of annuitypayments, the difference between areference rate and an agreed strike ratewhen the reference exceeds the strike.Commonly, the reference rate is three- orsix-month Libor. A cap is therefore a stripof interest rate guarantees that allows thepurchaser to take advantage of areduction in interest rates and to beprotected if they rise.They are priced asthe sum of the cost of the individualoptions, known as caplets. See also collar

Capital-protectedA structured product that provides capitalprotection offers an amount that at leastmatches a given proportion of theinvestor’s original capital input atmaturity. Can also be referred to asprincipal-protected.

Capital-protected credit-linked noteA credit-linked note where the principal ispartly or fully guaranteed to be repaid atmaturity. In a 100% principal-guaranteed

credit-linked note, only the coupons paidunder the note bear credit risk. Such astructure can be analysed as (i) a Treasurystrip and (ii) a stream of risky annuitiesrepresenting the coupon, purchased fromthe note proceeds minus the cost of theTreasury strip. See also credit-linked note

Capped floaterA floating-rate note which pays a coupononly up to a specified maximum level ofthe reference rate.This is done byembedding a cap in a vanilla note wherethe investor effectively sells the issuer acap. A capped floater protects the debtissuer from large increases in the interestrate environment.

Capped swap An interest rate swap with an embeddedcap in which the floating payments of theswap are capped at a certain level. Afloating-rate payer can thereby limit itsexposure to rising interest rates.

Caption An option on a cap. A type of compound option in which the purchaser has the right, but not theobligation, to buy or sell a cap at apredetermined price on a predetermineddate. Captions can be a cheap way ofleveraging into the more expensiveoption. See also floortion

Cash and carry When a contango exists, the premium of the forward position over


Glossary of terms

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Cthe spot generally reflects costs of buyingand holding (eg financing, transactioncosts, insurance, custody) for that period.See also cash and carry arbitrage

Cash market The physical market for buying andselling an underlying (eg equities, bonds),as opposed to a futures market.

Cash-and-carry arbitrage A strategy, used in bond or stock indexfutures, in which a trader sells a futurescontract and buys the underlying todeliver into it, to generate a riskless profit.For the strategy to work, the futurescontract must be theoretically expensiverelative to cash.

Cash-and-carry arbitrage and reversecash-and-carry arbitrage typically keepthe futures and underlying marketsclosely aligned. See also basis trading,reverse cash-and-carry arbitrage

Catastrophe bond A bond that pays a coupon that decreasesonly after a catastrophe such as ahurricane or earthquake with a specifiedmagnitude in a specified region andperiod of time.

Catastrophe option These options can be American-style orEuropean-style, either paying out if asingle specified catastrophe such as ahurricane or earthquake occurs, oralternatively, having a pay-out dependent on an index. For example,

the index may represent the number ofclaims received by property insurancecompanies.

Catastrophe risk swapAn agreement between two parties toexchange catastrophe risk exposures. Forexample, in July 2001 Swiss Re and TokyoMarine arranged a $450 million dealincluding three risk swaps: Japanearthquake for California earthquake,Japan typhoon for France storm andJapan typhoon for Florida hurricane.Swaps increase diversification and allow each of the parties to lower the amount of capital that theyneed to hold.

Chooser option A chooser option offers purchasers thechoice, after a predetermined period,between a put and a call option.The pay-outs are similar to those of a straddle but chooser options are cheaper because purchasers must choose before expiry whether they wantthe put or the call.

CliquetCliquet structures, which can also becalled ratchet structures, periodicallysettle and reset their strike prices,allowing users to lock-in potential profits on the underlying.With a cliquetthe payout is worked out from theperformance of the underlying asset in anumber of set periods during theproduct’s life. See also ladder options




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Cliquet option Also known as a ratchet or reset option. Apath-dependent option that allows buyersto lock-in gains on the underlying securityduring chosen intervals over the life timeof the option.The option’s strike price iseffectively reset on predetermined dates.Gains, if any, are locked in. So if anunderlying rises from 100 to 110 in yearone, the buyer locks in 10 points and thestrike price is reset at 110. If it falls to 97 inthe next year the strike price is reset atthat lower level, no further profits arelocked in, but the accrued profit is kept. Seealso ladder option, lookback option, movingstrike option, path dependent option

Closed-form solution Also called an analytical solution. Anexplicit solution of, for example, an optionpricing problem by the use of formulaeinvolving only simple mathematicalfunctions, such as Black-Scholes or Vasicekmodels. Closed-form models can usuallybe evaluated much more quickly thannumerical models, which are sometimesfar more computationally intensive.

Collar The simultaneous sale of an out-of-the-money call and purchase of an out-of-the-money put (or cap and floor in the case ofinterest rate options).The premium fromselling the call reduces the cost ofpurchasing the put.The amount saveddepends on the strike rate of the twooptions. If the premium raised by the saleof the call exactly matches the cost of the

put, the strategy is known as a zero costcollar. The combination of purchasing theput and selling the call while holding theunderlying protects the holder fromlosses if the underlying falls in price, at theexpense of giving away potential upside.See also cap, equity collar, impact forward,risk reversal, zero cost option

Collar swap A collar on the floating-rate leg of aninterest rate swap.The transaction is zerocost – the purchase of the cap is financedby the sale of the floor.The collarconstrains both the upside and thedownside of a swap.

Collared floaterA floating-rate note whose couponpayments are subject to an embeddedcollar.Thus the coupon is capped at apredetermined level, so the buyerforsakes some upside, but also floored,offering protection from a downturn inthe reference interest rate. Also known asa mini-max floater.

Collateralised bond obligation (Cbo)A multi-tranche debt structure, similar toa collateralised mortgage obligation. Butrather than mortgages, low-rated bondsserve as the collateral. See alsocollateralised mortgage obligation

Collateralised debt obligation (Cdo)Generic name for collateralised bondobligations, collateralised loanobligations, and collateralised mortgage


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Cobligations. See also collateralised mortgage obligation, synthetic collateraliseddebt obligation

Collateralised loan obligation (Clo)A structured bond backed by the loanrepayments from a portfolio of pooledpersonal or commercial loans,excluding mortgages.The structureallows a bank to remove loans from itsbalance sheet and so reduce its requiredcapital reserves, while retaining contactwith the borrowers and fees fromservicing the loans. See also collateralisedmortgage obligation

Collateralised mortgage obligation A type of asset-backed security, in thiscase backed by mortgage payments.Typically, such securities provide a higher return than normal fixed-ratesecurities but purchasers sufferprepayment risk if mortgage holdersredeem their mortgages. Because theright to redeem the mortgage iseffectively an embedded call, suchsecurities have negative convexity.See also collateralised bond obligation,collateralised debt obligation, collateralisedloan obligation

ComboSee risk reversal

Compound optionA compound option is an option on anoption.The tool allows the user to buy orsell an option at a fixed price during a set

period.They are often used to hedgeagainst increase in option prices duringvolatile periods. Examples includecaptions and floortions.

Condor The simultaneous purchase (sale) of anout-of-the-money strangle and sale(purchase) of an even further out-of-the-money strangle.The strategy limits theprofit or loss of the pay-out and isdirectionally neutral.

Constant maturity swapThis is an interest rate swap where thefloating interest arm is reset periodicallywith reference to longer durationtreasury-based instruments rather than amarket index such as LIBOR.

Constant maturity treasury derivativeOver-the-counter swaps and optionswhich use longer-term,Treasury-basedinstruments for their floating ratereference than money market indexes,such as Libor.‘Constant Maturity Treasury’(CMT) refers to the par yield that wouldbe paid by a treasury bill, note or bondwhich matures in exactly one, two, three,five, seven, 10, 20 or 30 years. Since theremay not be treasury issues in the marketwith exactly these maturities, the yield isinterpolated from the yields on treasuriesthat are available. In the US, such rateshave been calculated and published bythe Federal Reserve Bank of New York andthe US Treasury department on a dailybasis every day for more than 30 years.




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The H.15 Report from the Federal Reserve Bank is often used as a source forCMT rates.

It is then possible for this interpolatedyield to form the index rate forinstruments such as floating rate notes,which pay interest linked to the CMTyield, options, which pay the differencebetween a strike price and the CMT yield,and swaps and swaptions, in which one ofthe cashflows exchanged is the CMTyield.Where necessary, the reference rateis reset at each settlement date.Typicaluses of CMT derivatives as hedging toolsinclude the purchase of CMT floors bymortgage servicing companies to protectthe value of purchased mortgageservicing portfolios, and the purchase ofCMT caps to protect investors withnegatively convex mortgage-backedsecurities portfolios. It is possible to enterinto derivatives in other currencies thatare based, by analogy, on a ‘constantmaturity interest rate swap’ interpolatedfrom the swap curve in the relevantcurrency. Such derivatives are known asconstant maturity swap (CMS) derivatives.Unlike CMT derivatives, CMS derivativesincorporate the spread component of swaps.

Constant proportion portfolio insurance (CPPI)A fund management technique that aimsto provide maximum exposure to riskyassets while still protecting investors’capital.The technique requires themanager to dynamically rebalance the

portfolio between risky assets (such asequities) and safe assets (such as bonds)according to a quantitative model. Thelevel of risky assets is managed such thatat all times, in the event of a market crash,the remaining NAV of the fund is stillsufficient to meet the stated protectionlevel. Generally the proportion of RiskyAssets in the fund is increased whenthese perform well and decreased whenthese perform poorly.

The capital protection level may befixed, or rachet up (reset) according to acertain percentage of the fund NAVachieved during the fund term.

Contingent swap The generic term for a swap activatedwhen rates reach a certain level or aspecific event occurs. Swaptions areoften considered to be contingentswaps. Other types of swaps, forexample, drop-lock swaps, are activatedonly if rates drop to a certain level or if a specified level over a benchmark is achieved.

Contract for difference (Cfd) A Contract for Difference is typically anagreement made between two parties toexchange (at the closing of the contract)a cashflow equivalent to the differencebetween the opening and closing prices,multiplied by the number of sharesdetailed in the contract. CFDs are tradedon margin, do not incur stamp duty andcan have individual stocks or indexes asthe underlying.


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CConvergence tradeTrading strategy where similar securitiesare bought and sold simultaneously inthe expectation that prices will convergein an orderly fashion.11.. A way of taking advantage ofmispriced options by creating a syntheticshort futures position and hedgingmarket risk by buying a futures contractagainst it.Thus if a put is undervalued, atrader buys it, at the same time selling afairly valued call and buying a futurescontract.The same strategy can beapplied if the call is mispriced. If theoption is truly undervalued, the traderearns a riskless profit.The whole exerciserelies on put-call parity 22.. The act of converting a convertiblebond into equity. See also box, reversal

Convertible bond A bond issued by a company that may beexchanged by the holder for a number ofthat company’s shares at a predeterminedratio, or at a discount to the share price atmaturity. Because the convertible embedsa call option on the company’s equity,convertibles carry much lower rates ofinterest than traditional debt and aretherefore a cheap way for companies toraise debt.The problem for existingshareholders is that conversion dilutes thecompany’s outstanding shares.Typically,bonds are convertible into a company’sown stock.There are however ‘third partyconvertibles’, which convert into shares of another company. See also equity warrant, resettable convertible bond

Convexity A bond’s convexity is the amount that itsprice sensitivity differs from that impliedby the bond’s duration. Fixed-rate bondsand swaps have positive convexity: whenrates rise the rate of change in their price isslower than suggested by their duration;when rates fall it is faster. Positive convexityis therefore a welcome attribute.Thehigher the bond’s duration, the more itsconvexity. Bonds or swaps with call optionsor embedded call options, eg collateralisedmortgage obligations, have negativeconvexity: when rates rise their price fall isfaster relative to the interest rate move.Convexity effectively describes the sameattribute as gamma.

Correlation Correlation is a measure of the degree towhich changes in two variables are related.It is normally expressed as a coefficientbetween plus one, which means variablesare perfectly correlated (in that they movein the same direction to the same degree)and minus one, which means they areperfectly negatively correlated (in thatthey move in opposite directions to thesame degree). In financial marketscorrelation is important in three areas:11.. The model used for global assetallocation decisions, Sharpe’s capital assetpricing model (CAPM), has, as its linchpin,a covariance matrix that measurescorrelations between markets.22.. Correlation is also central to the pricingof some options, where two-factor ormulti-factor models are used. For spread




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options, yield curve options and cross-currency caps, estimating the correlationbetween the underlying assets is ofprimary importance, the degree ofcorrelation between them having a directinfluence on the option price. For quantossuch as guaranteed exchange rate options,or differential swaps, the correlation effectis the extent to which there is arelationship between movements in theunderlying and movements in the ex-change rate, which has a secondary effecton the price of the option.33.. Correlation between markets is alsoused to offset an option position in onemarket against another with similardirection and volatility. Such a strategymight be used to reduce cost – to avoidhedging the positions separately, orbecause implied volatility in the secondmarket is lower – or because hedging isdifficult in the first market. Correlation canbe estimated historically (like volatility)but tends to be unstable, and historicestimations may be poor predictors offuture realised correlations. See also joint option

Correlation swapAn instrument that allows an investor totake financial exposure on a set ofcorrelations.

Corridor floaterSee range note

Corridor optionThe holder of a corridor option receives a

coupon at the end of the lifetime of thecorridor whose magnitude depends uponthe behaviour of a specified spot rateduring the lifetime of the corridor. Foreach day on which the spot rate (typicallyan official fixing rate observation) remainswithin the chosen spot range (the accrualcorridor) the holder accrues one day’sworth of coupon interest.A variation is the knockout corridoroption. In this structure, the holder ceasesto accrue coupon interest as soon as thespot rate leaves the range. Even if the spotrate subsequently re-enters the range, theholder does not continue to accruecoupon interest. At the end of the option’slifetime, the accrued coupon is calculatedaccording to the following formula:

If the accrual corridor is one-sided (theother side of the range being open-ended), it is known as a wall option.Typically, corridor options are imbeddedin a structured note, sometimes called arange note, that pays a higher yield thanthe corresponding vanilla debt as long asthe underlying rate remains sufficientlylong within the accrual corridor. A similaroption to the corridor option is the rangebinary, a binary option which pays a fixedcoupon amount if the range is notbreached but nothing if it is breached.

Cost of carry The cost of financing an asset. If the costis lower than the interest received, theasset has a positive cost of carry; if higher,the cost of carry is negative.The cost ofcarry is determined by the opportunities


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Cfor lending the asset and the shape of theyield curve. So a bond, for example, wouldhave a positive cost of carry if short-termrates (financing rates) were lower thanthe assets’s yield or (and) if the cost couldbe mitigated by lending out thesecurities. See also future

Counterparty credit riskSee credit risk

Covered call To sell a call option while owning theunderlying security on which the optionis written. The technique is used by fundmanagers to increase income byreceiving option premium. It would beused for securities they are willing to sell,only if the underlying went upsufficiently for the option to beexercised. Generally, covered call writerswould undertake the strategy only ifthey thought volatility was overpriced inthe market. The lower the volatility, theless the covered call writer gains inreturn for giving up upside in theunderlying. It provides downsideprotection only to the extent that theoption premium offsets a marketdownturn. See also covered put

Covered put To sell a put option while holding cash.This technique is used to increaseincome by receiving option premium. Ifthe market goes down and the option isexercised, the cash can be used to buythe underlying to cover. Covered put

writing is often used as a way of targetbuying: if an investor has a target price atwhich he wants to buy, he can set thestrike price of the option at that level andreceive option premium to increase theyield of the asset. Investors also sellcovered puts if markets have fallenrapidly but seem to have bottomed,because of the high volatility typicallyreceived on the option.See also covered call

Covered warrant See warrant

Cox-Ingersoll-Ross model In its simplest form this is a lognormalone-factor model of the term structure ofinterest rates, which has the short rate ofinterest as its single source of uncertainty.The model allows for interest rate meanreversion and is also known as the squareroot model because of the assumptionsmade about the volatility of the short-term rate.The model provides closed-form solutions for prices of zero-coupon bonds, and put and call optionson those bonds.

Credit default swapA bilateral financial contract in which onecounterparty (the protection buyer orbuyer) pays a periodic fee, typicallyexpressed in basis points per annum onthe notional amount, in return for acontingent payment by the othercounterparty (the protection seller orseller) upon the occurrence of a credit




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event with respect to a specifiedreference entity.The contingent payment is designed to mirror the lossincurred by creditors of the referenceentity in the event of its default.The settlement mechanism may be cashor physical. See also basket credit default swap

Credit derivativeA bilateral financial contract, whichisolates credit risk from an underlyinginstrument and transfers that credit riskfrom one party to the contract (theprotection buyer) to the other (theprotection seller).There are two maincategories of credit derivatives: the firstconsists of instruments such as creditdefault swaps in which contingentpayments occur as a result of a creditevent; the second, which includes creditspread options, seeks to isolate the creditspread component of an instrument’smarket yield.

Credit eventAny one of a specified set of events,which, if occurring with respect to anobligation of the reference entityspecified in a credit default swap, willtrigger contingent payments.Applicable events, which generallyinclude bankruptcy,repudiation/moratorium, restructuring,failure to pay, and cross-acceleration are determined by negotiation betweenthe parties at the outset of a creditdefault swap.

Credit optionPut or call options on the price of either(a) a floating rate note, bond, or loan, or(b) an asset swap package, consisting of acredit-risky instrument with any paymentcharacteristics and a correspondingderivative contract that exchanges thecashflows of that instrument for a floatingrate cashflow stream, typically three- orsix-month Libor plus a spread.

Credit riskAlso known as default risk. In broad terms,the risk that a loss will be incurred if acounterparty to a (derivatives) transactiondoes not fulfil its financial obligations in atimely manner.The term is sometimesloosely used as shorthand for thelikelihood or probability of default,irrespective of the value of any positionexposed to this risk. More precisely, creditrisk is the risk of financial loss arising out ofholding a particular contract or portfolio.

Credit spreadA credit spread is the difference in yieldbetween two debt issues of similarmaturity and duration.The credit spreadis often quoted as a spread to abenchmark floating-rate index such asLibor, or alternatively as a spread to ahighly rated reference security such as agovernment security.The credit spread isoften used as a measure of relativecreditworthiness, with reduction in thecredit spread reflecting an improvementin the borrower’s perceivedcreditworthiness.


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CCredit spread forwardA cash-settled forward contract withsettlement amounts based on the creditspread between two predetermined debtissues on the maturity date. See also creditspread option

Credit spread optionAn option on the credit spread betweentwo debt issues.The option will pay outthe difference between the credit spreadat maturity and a strike spreaddetermined at the outset. See also creditspread forward

Credit-linked noteA security with redemption and/orcoupon payments linked to theoccurrence of a credit event with respectto a specified reference entity. In effect, acredit-linked note embeds a creditdefault swap into a funded asset to createa synthetic investment that replicates thecredit risk associated with a bond or loanof the reference entity. Credit-linkednotes are typically issued on anunsecured basis directly by a corporation or financial institution. Credit-linked notes may also be issued from acollateralised Special Purpose Vehicle(SPV). See also capital-protected credit-linked note

Cross-currency cap A cap in which the vendor will pay thepurchaser the spread between interestrates (usually Libor-based) in differentcurrencies minus a strike spread, where

this exceeds zero, in return for apremium. It has the same relationship toa differential swap as a cap has to aninterest rate swap. See also cross-currency floor

Cross-currency floorThis is an option setting a cap on thespread between two index interest ratesin different currencies. See also cross-currency cap

Cross-currency swap A cross-currency swap involves theexchange of cashflows in one currency forthose in another. Unlike single-currencyswaps, cross-currency swaps often requirean exchange of principal.Typically thenotional principal is exchanged atinception at the prevailing spot rate.Interest rate payments are then passedback on a fixed, floating or zero basis.Theprincipal is then re-exchanged at maturityat the initial spot rate.

Cumulative capA cumulative interest rate cap protectsagainst increases in total interest expenseover a specified period of time.Thisperiod of time will incorporate severalrate settings in determining the finalinterest expense (for example, four three-month Libor settings for an annualinterest expense amount).This differsfrom a standard cap, which caps anabsolute rate of interest in eachcalculation period. Because a cumulativecap does not provide the period-to-




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period protection of a standard cap, it isgenerally cheaper than thecorresponding standard cap.

Currency forward An agreement to exchange a specifiedamount of one currency for another at afuture date at a certain rate.The exchangeof currencies is priced so as to allow norisk-free arbitrage. In other words, pricingis not a market estimate of the spot rateat that date, but is made according to thetwo currencies’ respective interest rates.For example, assuming that Eurosterlinginterest rates are 10% and Eurodollar 5%,and the US dollar/sterling spot rate is1.75, the forward rate should reflect the5% interest rate advantage of depositingmoney in sterling.Thus the 12-monthforward rate should be 1.6695.Forwards are more appropriate thanoptions if a company has a strongdirectional view of expected movementsin exchange rates. But certainty is rare andhedging entirely with forwards may leavea company locked into unfavourableexchange rates. Unlike options, forwardsdo not enable companies to takeadvantage of favourable currencymovements.The purchaser of a forward,unlike the purchaser of a future, carriesthe credit risk of the firm from which itmakes the purchase. Since the contractsare not easily reassignable, it is difficult toreduce this risk.

Currency overlay See overlay

Currency protected optionThe same as guaranteed exchange rate orquanto option.

Currency riskCurrency risk arises from changes in thevalue of currencies. For example, if acompany receives a portion of its incomein a foreign currency, it is exposed tochanges in the value of that currency. Riskmanagement and derivatives can be usedto minimise this risk.

Currency struck optionThis is the same as joint option.

Current exposureAnother name for replacement cost.

CylinderSee risk reversal

DDeferred payout option A deferred payout option is a variationon American-style options similar to ashout option. The holder of the optionmay exercise it at any time, for the valuetaken by the underlying at that time,but the payout is delayed until theexpiry date. This term is also applied tocertain digital options whose payout isnot paid when triggered, but deferreduntil the final maturity. See also option styles


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DDeferred start option See forward start option

Delayed reset swap Also known as an in-arrears swap. A swapin which floating payment is based on thefuture, rather than present, value of thereference rate. For six-month delayedLibor reset swaps, for example, instead offixing Libor six months and two daysbefore the payment date, the floating-rateborrower delays fixing until two daysbefore payment. Such swaps are popular in a steep yield curveenvironment, when a fixed-rate receivermay think rates will not rise as fast as theyield curve predicts.

Delta The delta of an option describes itspremium’s sensitivity to changes in theprice of the underlying. In other words, anoption’s delta will be the amount of theunderlying necessary to hedge changesin the option price for small movementsin the underlying.The delta of an optionchanges with changes in the price of theunderlying. An at-the-money option willhave a delta of close to 50%. It falls forout-of-the-money options and increasesfor in-the-money options, but the changeis non-linear: it changes much fasterwhen the option is close-to-the-money.The rate of change of delta is an option’s gamma.

Delta hedging An option is said to be delta-hedged if a

position has been taken in the underlyingin proportion to its delta. For example, ifone is short a call option on an underlyingwith a face value of $1 million and a deltaof 25%, a long position of $250,000 in theunderlying will leave one delta-neutralwith no exposure to small changes in theprice of the underlying. Such a hedge isonly effective instantaneously, however.Since the delta of an option is itself alteredby changes in the price of the underlying,interest rates, the option’s volatility and itstime to expiry, changes in any of thesefactors will shift the net position awayfrom delta-neutrality. In practice,therefore, a delta-hedge must berebalanced continuously if it is to beeffective. See also static replication

DerivativeA derivative instrument or product is onewhose value changes with changes inone or more underlying market variables,such as equity or commodity prices,interest rates or foreign exchange rates.Basic derivatives include: forwards,futures, swaps, options, warrants andconvertible bonds. In mathematicalmodels of financial markets, derivativesare known as contingent claims.

Difference optionSee spread option

Diffusion process A continuous-time model of the behaviourof a random variable. An example of such amodel is Generalised Brownian Motion




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(GBM), which is often used to model thebehaviour of spot rates.

Digital optionDigital options pay a set amount if theunderlying asset is above, or sometimesbelow, a certain level on a specific date.These options have only two possibleoutcomes: a set payout, or nothing at all.Thus, they are also known as binary or all-or-nothing options.

Digital swapA swap in which the fixed leg is only paidon each swap settlement date if theunderlying has met certain triggerconditions over the period since theprevious payment date. Nothing is paid ifthis is not the case.The premium for sucha swap is amortised over the maturity ofthe swap and an instalment paid at eachpayment date.

Discrete barrier optionBarrier options where the trigger level isonly active for part of the option’slifetime.This includes barrier optionswhere the trigger is only valid on certainfixing dates, as well as cases where thetrigger is valid for sub-intervals of theoption’s lifetime. See also barrier option

DistributionThe probability distribution of a variabledescribes the probability of the variableattaining a certain value. Assumptionsabout the distribution of the underlyingare crucial to option models because the

distribution determines how likely it isthat the option will be exercised. Manymodels assume the logarithm of therelative return has a normal distribution,which can be described by twoparameters. The first is the distribution’smean; the second its standard deviation(equivalent, if annualised, to volatility). Inpractice, most empirically observed assetdistributions depart from normality.Thisdeparture can be described in terms ofthe skew (how much it tilts to one side orthe other) and kurtosis, which describeshow fat or thin are the tails at either side.Most markets tend to have fat tails (to beleptokurtic) rather than thin tails(platykurtic).This pushes up the price ofout-of-the-money options.

Double barrier optionThis is an option with two barriers; onesetting the upper limit of the price of theunderlying and one setting the lowerlimit. If the underlying crosses either ofthese barriers the option is eitheractivated (knock-in) or deactivated(knock-out). See also barrier option.

Double no-touchA double no-touch option pays a setamount as long as one of two specifiedbarrier levels are not broken during the life of the option.This tool is popular forusage in relatively stable markets.

Downside riskThe risk the investor is exposed to if thereis a fall in the value of the underlying.


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D/EDual currency swap Dual currency swaps are currency swapsthat incorporate the foreign exchangeoptions necessary to hedge the interestpayments back into the principalcurrency for dual currency bonds.

Dynamic hedgingSee delta hedging

E Embedded option An option, often an interest rate option,embedded in a debt instrument thataffects its redemption. Examples includemortgage-backed securities and callableand puttable bonds. Embedded optionsdo not have to be interest rate options;some are linked to the price of an equityindex (Nikkei 225 puts embedded inNikkei-linked bonds) or a commodity(usually gold). Many so-called guaranteedproducts contain zero-coupon bonds andcall options.

Equilibrium model A model that specifies processes for theunderlying economic variables and theextra risk premium investors require for risky assets.The evolution of asset pricesand their risk premiums can then bederived from the model thus specified.

Equity (index) swap A swap in which the total or price return

on an equity index, equity basket orsingle equity is exchanged for a stream ofcashflows based on a short-term interestrate index (or another index).

Equity swaps are a convenientstructure for switching into or out ofequity markets, particularly for those thatprefer to avoid, or are not allowed to use,stock index futures. Like futures, the priceof the swap is directly related to the costof carry, although there may also be tax considerations.

Equity collar Equity collars are used by investors keen toreduce their downside risk. An equity collaris formed by buying an equity put optionwith a strike price below the current valueof the equity, at the same time as selling anequity call option with a strike above thecurrent equity price.Thus a collar isimposed around the investor’s equityposition. If the value of the underlyingequity falls through the strike of thebought put, it can be exercised to limitlosses. However, if the underlying stockrises through the strike of the sold call, theinvestor may have to deliver the equity atthe strike, thus foregoing potentialadditional upside.See also collar

Equity knock-out swap An interest rate or cross-currency swapthat gets terminated (knocked-out) if agiven stock or equity-index reaches aspecified trigger level between inceptionand expiry.The knock-out can be unconditional once the pre-determined




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equity level is reached, or the client canbe given the choice to cancel the swapshould the trigger level be reached.

Equity linked noteAn equity linked note is a tool that islinked to a single equity, equity index orbasket of equities.They may or may notbe principal protected.

Equity warrant A warrant is a financial instrument issuedby a bank or other financial institutions,which is traded on a stock exchange’sequity market.Warrants may be issuedover securities such as shares in a company,a currency, an index or a commodity.

A call warrant gives the holder theright (but not the obligation) to buy agiven security at a given price known asthe exercise price, on a given date, knownas the expiry date. Conversely a putwarrant gives the holder the right to sellthe security at the exercise price on theexpiry date.These instruments aresometimes known as covered warrants orderivative warrants. See also convertiblebond, warrant

European-style optionEuropean-style options can only be exercised on their expiry date.They standin contrast to American-style options,which can be exercised at any time until maturity.

Everest structureA capital guaranteed structure generally

offering the investor the sum invested atmaturity and potential upside linked tothe performance of the least-performingasset in a predefined basket.The Evereststructure may also pay coupons over its life.

Exchangeable bondThese are just like convertible bonds.Themain difference is that these are typicallyissued on stock, which is not the stock ofthe issuing firm.

Exchange-traded option See option

Exercise See option

Exotic optionAny option with a more complicatedpayout structure than a plain vanilla putor call option.The payout of a plain vanillaoption is simply the difference betweenthe strike price of the option and the spotprice of the underlying at the time ofexercise. For a European-style option, theexercise time is always the expiry date;other option styles offer greater flexibility.There are a number of ways in which anoption payout can differ from that of aplain vanilla.The payout could also be afunction of:■■ the difference between a strike and an

average rate for the underlying(average options)

■■ the difference between prices for twodifferent underlyings (difference


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E/Foptions, exchange options), the sameunderlying at different times (high-low options)

■■ the correlation between two or moreunderlyings (outperformance options,outside barrier options)

■■ the difference between a strike and thespot rate at some time other thanexpiry (deferred payout options, shoutoptions, lookback options, cliquetoptions, ladder options)

■■ a fixed amount (binary options)Alternatively, or additionally, a payout

may be conditional on certain triggerconditions being met. For example, barrieroptions are activated or nullified if a spotrate falls or rises through a predeterminedtrigger level. Multiple trigger conditionsare possible (as in the case of corridor ormini-premium options).

Exploded tree A tree (binomial or trinomial) in which anup step followed by a down step gives adifferent outcome to a down stepfollowed by an up step. Consequently, thenumber of nodes increases exponentially,compared with a recombining tree, inwhich the number increasesquadratically.This makes their evaluationexceptionally computer-intensive.The advantage is that they can be used toprice path-dependent options and theyare important for modelling interest rate options.

Extreme value theoryAn area of statistical research that focuses

on modelling the extreme values ofreturn distributions.This is important infinance because many models (forexample the Black-Scholes Model)assume that the distribution of returns islog-normal. However, real-worlddistributions are found to have fat-tails –implying that rare events such as crashesare more likely than the traditionaltheories suggest.

FFat tailsSee kurtosis

Financial engineering The design and construction ofinvestment products to achieve specified goals.

Flexible optionA flexible option (also known as a flexibleexchange or flex option) is a customisableexchange-traded option, which allows thebuyer to customise contract terms suchas expiry date and contract size inaddition to the strike price. Flexibleoptions with single stock, index, or evencurrency underlyings are traded onseveral major exchanges.

Floor fundAlso known as a ratchet fund. A particulartype of structured product that aims todeliver minimum returns, which usually




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are at least equal to the sum invested,plus some additional upside based on theperformance of the stock market.However, unlike guaranteed funds, veryfew floor funds come with a contractualguarantee. Many floor funds are managedusing the technique of constantproportion portfolio insurance (CPPI).

Floortion An option on a floor.The purchaser hasthe right, but not the obligation, to buy orsell a floor at a predetermined price on apredetermined date. See also caption

Forward See future

Forward rate agreement A forward rate agreement (FRA) allowspurchasers/sellers to fix the interest ratefor a specified period in advance. Oneparty pays fixed, the other an agreedvariable rate. Maturities are generally outto two years and are priced off theunderlying yield curve.The transaction isdone on a nominal amount and only the difference between contracted and actual rates is paid. If rates have risen by the time of the agreement’smaturity, the purchaser receives thedifference in rates from the seller and vice versa. A swap is therefore a strip of FRAs. FRAs are off-balance sheet – there are no up-front or marginpayments and the credit risk is limited tothe mark-to-market value of thetransactions. Unlike interest rate swaps,

FRAs settle at the beginning of theinterest period, two business days afterthe calculation date.

Forward start option An option that gives the purchaser theright to receive, after a specified time, astandard put or call option.The option’sstrike price is set at the time the option isactivated, rather than when it ispurchased.The strike level is usually set ata certain fixed percentage in or out-of-the-money relative to the prevailing spotrate at the time the strike is activated.

Forward swap A swap in which rates are fixed before thestart date. If a company expects rates torise soon but only needs funds later, itmay enter into a forward swap.

FrationSee interest rate guarantee

Future A future is a contract to buy or sell astandard quantity of a given instrument,at an agreed price, on a given date. Afuture is similar to a forward contract anddiffers from an option in that both partiesare obliged to abide by the transaction.Futures are traded on a range ofunderlying instruments includingcommodities, bonds, currencies andstock indexes.

The most important differencebetween futures and forwards is thatfutures are almost always traded on an


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F/Gexchange and cleared by a clearinghouse, whereas forwards are over-the-counter instruments. Furthermore,futures, unlike forwards, have standarddelivery dates and trading units. Mostfutures contracts expire on a quarterlybasis. Contracts specify either physicaldelivery of the underlying instrument orcash settlement at expiry. Cashsettlement involves the company payingor being paid the difference between theprice struck at the outset and the expiryprice of the contract. See also cost of carry,implied repo rate

Future rate agreement See forward rate agreement

Futures optionAn option, either a put or a call, on anyfutures contract. Also known as an optionon a future.

GGamma The rate of change in the delta of anoption for a small change in theunderlying.The rate of change is greatestwhen an option is at-the-money anddecreases as the price of the underlyingmoves further away from the strike pricein either direction. A long gammaposition is one in which a trader is longoptions. For a position that is shortgamma, the opposite holds. Gamma can

be hedged by mirroring the optionsposition. Alternatively, a trader maychoose to adjust the position in the underlying continually in order tomaintain delta neutrality. See also vega

Garman-Kohlhagen Model A model developed to price European-style options on spot foreign exchangerates.The model is based upon the Black-Scholes model with the addition of an extra interest rate factor for theforeign currency.

Geared barrier optionA type of in-the-money barrier optionwhere the barrier is in-the-money and liesbetween the strike and the underlyingspot rate.

GearingGearing refers to the degree of exposureof a product to movements in theunderlying index. A product with 100%gearing would have returns exactly equalto any rise in the index. A product’sgearing is also called participation.

Geometric Brownian motion Geometric Brownian motion is a modelfrequently used for the diffusion processfollowed by asset prices. StandardBrownian motion is a random walk processwith Gaussian increments; that is, changesin the asset price are normally distributed.The term geometric means it is theproportional change in the asset price (asopposed to the absolute level) that is




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normally distributed.This gives the modeluseful properties, in that the asset pricecannot be negative, and that the logarithmof the asset price will be normallydistributed, making the model analyticallytractable.See also stochastic process

Global floorA term usually associated with cliquetproducts. A cliquet product with globalfloor will provide a minimum return thatis at least equal to the principal invested.Some cliquet products can haveguaranteed principal redemption of morethan 100%.

Growth productA term used to describe a type ofstructured product whose payouts areonly made at maturity with no incomestream during the product life. A growthproduct can be either principalguaranteed or non-guaranteed, althoughthe former is common.

Guarantee levelThe amount of principal that isguaranteed to be repaid at the maturityof the product.

Guaranteed couponCoupon payments that are guaranteed bythe guarantor, and are paid during the life of the product irrespective ofperformance of the underlying.

Guaranteed exchange rate option An option (also known as a quanto

option) on an asset in one currencydenominated in a second currency. Theexchange rate at which the purchaserconverts the currency is fixed at the start.Such options are popular as investorswant exposure to foreign assets withoutthe foreign exchange risk. The extra costof the option depends on the correlation between movements in the exchange rate and movements inthe underlying. The higher (morepositive) the correlation between theunderlying and the exchange rate(expressed as the number of units ofcurrency two per unit of currency one)the more expensive a call option will beand the cheaper a put option will be.Quanto options can, however, lookcosmetically cheaper (or more expensive)depending on the forward interest ratesin the two currencies. For example,buying a call on a US asset could be moreexpensive in euros if there is a wideinterest rate differential between theeuro and the dollar. See also joint option,quanto product

Guaranteed fundA guaranteed fund comes with a promise by the guarantor to repay aportion, usually 100% of the principal atmaturity. Guaranteed funds can alsoincorporate guaranteed coupons payable regardless of the underlyingperformance and/or non-guaranteedcoupons linked to the performance ofunderlying assets, often a stock index or basket of stocks.‘Guaranteed’


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G/Hdoes not mean the investment is risk-free. The guarantee on principalrepayment usually holds only when theproduct is held to maturity, and is subjectto credit risk of the guarantor. Investorswho redeem early are usually repaid atnet asset value and thus subject tomarket risk. A guaranteed fund isconstructed by investing part of theproceeds in a zero-coupon bond or otherfixed income instrument – whichunderwrites the guaranteed payment atmaturity – and the rest of the money inan embedded call or put option on theunderlying for additional returns. Hence,investors also run counterparty risk inrelation to the option strategy. Aguaranteed structure can also take theform of a guaranteed note or guaranteed bond. Generally, anystructured product with a promise toreturn 100% of the principal invested at maturity can be considered aguaranteed product.

Guaranteed return on investment Any instrument (usually a structurednote) which guarantees investors aminimum return on their investment.Thiscan be achieved by combining a debtissue with a structure, such as a collar orcylinder, which locks gains into a range.This means that the investor gainsprotection from an adverse market move by limiting participation in anyfavourable move.See also principal-guaranteed product

HHaircut The excess of an asset’s market value overeither the loan for which it can serve asadequate capital, or the regulatory capitalvalue. It can also refer to the dealer’scommission on a transaction.

Hard protectionA term sometimes used to refer to the level of capital protection provided ina high-income type of structuredproduct. A hard protection level of 90%means that so long as the index or basket of shares is above 90% of thestarting level, the investor’s capital willnot be at risk.

Heath-Jarrow-Morton modelA multi-factor interest rate model, whichdescribes the dynamic of forward rateevolution. An extension of the Ho-Leemodel, the underlying is the entire termstructure of interest rates.The approach isvery similar to the original Black-Scholesmodel: it does not model qualities such asthe ‘price for risk’.

The model requires two inputs: theinitial yield curve and a volatility structurefor the forward.The volatility is onlyspecified in a very general form. Bychoosing an appropriate volatilityfunction, it is possible to reduce HJM tosimpler models such as Ho-Lee, Vasicek,and Cox-Ingersoll-Ross.




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The practical importance of the HJMmodel is that it provides a singlecoherent framework for pricing andhedging an entire book of instruments (including instruments such as caps and swaptions) and is notexcessively computationally intensive. Research building on HJM(such as the market model) hasconcentrated on widening its scope toremove the possibility of negativeinterest rates, include more than oneinterest rate curve and incorporatedefault risk.

HedgeTo hedge is to reduce risk by makingtransactions that reduce exposure tomarket fluctuations; for example, aninvestor with a long equity position might compensate by buying put options to protect against a fall inequity prices. A hedge is also the term for the transactions made to effect this reduction.

High-coupon swap A swap in which the fixed-rate paymentsare above market rates. (Also known as a premium swap.)

High-income productA type of structured product that pays anincome that is well above the rate ofinterest on conventional fixed-ratedeposits. Generally, the higher the rate ofreturn offered on a product, the higherthe degree of risk.

High-low option A combination of two lookback options. Ahigh-low option pays the differencebetween the high and low of anunderlying, such as a stock index. Aspeculative purchaser would be taking the view that the market would be more volatile than the impliedvolatilities of both lookback optionsincorporated in the structure. See alsopath-dependent option

Hindsight optionSee lookback option

Historic rate rolloverA historic rate rollover allows an existing currency forward or spot position to be rolled forward withoutgenerating any intermediate cash flows.Effectively the position is reinstated for anew settlement date using a new off-market forward rate based on the historic rate.

Historical volatility Historical volatility is a measure of thevolatility of an underlying instrumentover a past period. Historical volatility canbe used as a guide to pricing options butisn’t necessarily a good indicator of futurevolatility.Volatility is normally expressedas the annualised standard deviation ofthe log relative return.

Ho-Lee model The first model that set out to modelmovements in the entire term structure


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H/I of interest rates, not just the short rate, in a way that was consistent with the initially observed term structure. However, since the model only has a single random factor, it makesthe simplifying assumption that thevolatility structure remains constantalong the yield curve. Heath-Jarrow-Morton later generalised this model,using a more general form of volatilityand introducing continuous trading.In addition, Ho-Lee allows for thepossibility of negative interest rates.The model was developed using abinomial tree, although closed-formsolutions have now been found fordiscount bonds and discount bond options.

Hull-White model An extension of the Vasicek model for interest rates, the main differencebeing that mean reversion is time-dependent. Both are one-factormodels.The Hull-White model wasdeveloped using a trinomial lattice,although closed-form solutions forEuropean-style options and bond prices are possible.

Hybrid productsHybrid products are constructed from a combination of interest rate,commodity, equity, credit and currencyderivatives.

Hypothecation The posting of collateral.

IImpact forward A collared forward, such as one in whichthe purchaser buys a put and sells a call,both being out-of-the-money.Thepremiums on the two options balanceout, so the strategy is zero cost. See also collar

Implied distributionThe probability distribution of returns foran asset, which is implied by optionstraded on that asset. The distribution isinferred by combining the variation ofvolatility with strike price (see volatility smile) and the assumptionsmade about the distribution in theoption pricing model.

Implied forward curve The forward curve implied by forwardrate agreements (derived from the parcurve) of various maturities. It is usuallysteeper than the spot yield curve.

Implied repo rate The return earned by buying a cheapest-to-deliver bond for a bond futurescontract and selling it forward via thefutures contract. See also future

Implied volatility The value of volatility embedded in an option price. All things being equal,higher implied volatility will lead to




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higher vanilla option prices and viceversa.The effect of changes in volatilityon an option’s price is known as vega. Ifan option’s premium is known, its impliedvolatility can be derived by inputting allthe known factors into an option pricingmodel (the current price of theunderlying, interest rates, the time tomaturity and the strike price).The modelwill then calculate the volatility assumedin the option price, which will be themarket’s best estimate of the futurevolatility of the underlying. See also option,volatility skew, volatility term structure

In-arrears swapSee delayed reset swap

Income productA term used for any type of structuredproduct that provides a periodic paymentof income.The rate of income is oftenhigher than the general rate of interestavailable on fixed-rate deposits andtherefore there may be a risk the initialcapital invested will not be returned in full.

Index amortising swap (Ias)An interest rate swap whose principalamortises on the back of movements inan index, such as Libor or constantmaturity treasuries.The fixed-rate receivereffectively grants an option to the fixed-rate payer to amortise the swap.The option is triggered by interest ratemovements after an initial lock-outperiod.The notional principal amortisesas rates fall or remains constant if rates

remain the same. In return for grantingthe option, the fixed-rate receiver gets ayield above current fixed rates. IAS havebeen widely used by US regional banks intheir asset/liability managementactivities. By using IAS, banks were able toobtain the negative convexity of amortgage-backed security and avoid therisk of excessive prepayments due tochanges in consumer sentiment. But thefixed receiver is exposed to both fallingand rising rates. If rates fall, there is thepossibility at each interest date that someor all of the swap will be terminated,creating a reinvestment risk. If rates rise,the swap may run to maturity, providingmeagre income while floating rates soar.

An IAS fixed-rate receiver is sellingvolatility to the payer for an enhancedyield. So the lower the volatility of theindex, the lower the option value andyield pick-up. A subsequent fall involatility benefits the receiver becausethe likelihood that the swap will amortisedecreases. IAS can be structured withnegative or positive convexity and theamortisation schedules and lock-outperiods can be changed in order toincrease or decrease yields. Also known asan Indexed principal swap. See alsomortgage swap

Index arbitrage See stock index arbitrage

Indexed strike capA cap for which the payout level isindexed to the level of the reference rate.


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IFor example, such a cap might be struckat 7.5% as long as the reference rateremained below 9%, but rise to 8.5% ifthe reference rate exceeded 9%. Anindexed strike cap is cheaper than aconventional cap.

Initial index levelMost structured products incorporatepayouts that are linked to the movementof an underlying index or share.Thisperformance is measured relative to thelevel of the underlying recorded at thestart of the investment term, or the initialindex level.

Integrated hedgeA hedge that combines more than onedistinct price risk. For example, crude oil isusually priced in US dollars.Therefore aproducer of crude oil whose homecurrency is not the dollar (say, the euro) isexposed to both currency risk and theprice risk for crude oil. One possibleintegrated hedge would be a singlequanto option, which would hedge theprice of crude oil in euro. As such, it woulddepend heavily on the correlation (if any)between the two markets.

Interest rate corridorAn interest rate corridor is composed of along interest rate cap position and ashort interest rate cap position. The buyerof the corridor purchases a cap with alower strike while selling a second capwith a higher strike. The premium earnedon the second cap then reduces the cost

of the structure as a whole. The buyer ofthe corridor is protected from rates rising above the first cap’s strike, butexposed if they rise past the second cap’s strike. It is possible to limit thisliability by selling a knock-out cap rather than a conventional cap. Thestructure is then known as a knock-outinterest rate corridor.

Interest rate guarantee An option on a forward rate agreement(FRA), also known as a FRAtion.Purchasers have the right, but not theobligation, to purchase an FRA at apredetermined strike. Caps and floors arestrips of IRGs.

Interest rate swap An agreement to exchange net futurecashflows. Interest rate swaps mostcommonly change the basis on whichliabilities are paid on a specified principal.They are also used to transform theinterest basis of assets. In its commonestform, the fixed-floating swap, onecounterparty pays a fixed rate and theother pays a floating rate based on areference rate, such as Libor.There is noexchange of principal – the interest ratepayments are made on a notionalamount. In floating-floating swaps thetwo counterparties pay a floating rate ona different index, such as three-monthLibor versus six-month Libor.

Swaps usually extend out as far as 10years, although 12–40 year maturities areavailable in some liquid currencies.




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However, the longer the maturity of theswap, the less liquid it becomes and creditrisk increases. Credit enhancements suchas mutual put options and collateral areused to ameliorate the credit risk oflonger term swaps. Interest rate swapsprovide users with a way of hedging theeffects of changing interest rates. Forexample, a company can convert floating-rate interest payments to fixed-ratepayments if it thinks interest rates will rise(which would make its liabilities moreexpensive). Companies can also useinterest rate swaps in conjunction withnew debt issuance, raising money on, say,a fixed basis and swapping it intofloating-rate debt. In an interest rate swapthere is a fixed-rate payer (floating-ratereceiver) and a fixed-rate receiver(floating-rate payer).

Interest-rate capSee cap

In-the-money Describes an option whose strike price isadvantageous compared with thecurrent forward market price of theunderlying. The more an option is in-the-money, the higher its intrinsicvalue and the more expensive itbecomes. As an option becomes more in-the-money, its delta increases and itbehaves more like the underlying inprofit and loss terms; hence deep in-the-money options will have a delta of closeto one. See also at-the-money, out-of-the-money

Intrinsic value The amount by which an option is in-the-money, that is, its value relative to thecurrent forward market price. Optionpremiums comprise intrinsic value andtime value.

Inverse floaterThe payments made on an inversefloating rate note (‘floater’) decrease as the reference interest rate increases, the reverse of the typical casewhere the payments rise with thereference rate.

The purchaser of an inverse floatingrate note is in effect selling interest ratecaps – this will increase the couponpayments in a stable or lower interest rateenvironment, but reduce them shouldinterest rates rise. Typically, the paymentis found by a fixed rate minus two timesthe reference rate.The floater can befurther leveraged by using a multiplierhigher than two.

JJoint optionAn option on an underlying, often a stockindex, denominated in a secondcurrency. Unlike a guaranteed exchangerate option, in which exchange rates arefixed, the purchaser of a joint call optionbenefits from upside in the currency inwhich the asset is originallydenominated, for example, S&P 500 call


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J/Koption struck in euro. In this case, at the inception, strike is specified in euro. At the maturity, S&P 500 level isobserved and is multiplied by thencurrent euro/US dollar rate. Thisconverted value of S&P 500 is compared with the strike to determinethe payout in euro. See also correlation,guaranteed exchange rate option, quanto product

Jump diffusionOne of the key assumptions of the Black-Scholes model is that the assetprice follows geometric Brownian motion with constant volatility andinterest rates. In a jump diffusion model, it is assumed that, in addition to this regular diffusion,there are jumps in the market. This type of model is sometimes used formodelling equities and emerging market currencies.

KKickerA kicker is a bonus payment that issometimes made when a structuredproduct matures if the value of theunderlying asset has risen enough.

Knock-inProducts which knock-in begin workingwhen the underlying passes through apredetermined spot rate or barrier

level. Knock-in options are a kind ofbarrier option.

Knock-outProducts which knock-out terminatewhen spot passes through apredetermined barrier level.Knock-out options are a kind of barrier option.

Knock-out interest rate corridorA corridor in which a client purchases astandard cap with a lower strike and sellsa knock-out cap with a higher strike(rather than selling a conventional cap).This means that the client is protectedfrom an increase in interest rates up to thestrike level for the knock-out cap, butexposed if rates rise beyond that level.However, the client is protected onceagain if the rates rise above the knock-outlevel, as the short knock-out cap will thenbe extinguished.

Kurtosis A measure of how fast the tails or wingsof a probability distribution approachzero, evaluated relative to a normaldistribution. The tails are either fat-tailed(leptokurtic) or thin-tailed (platykurtic).Markets are generally leptokurtic. Thefatter the tails, the greater the chance avariable will reach an extreme value,implying that models such as Black-Scholes – which assume perfect normal distribution – produce pricingbiases for deep in- or out-of-the-money options.




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LLadder optionA path-dependent option, most oftenbased on an equity index or a foreignexchange rate.The payout of a ladderoption increases stepwise as theunderlying trades upwards (ordownwards) through specified barrierlevels (the ‘rungs’ of the ladder). Each timethe underlying trades through a newbarrier level, the option payout is locked-in at the higher level. See also cliquet,cliquet option, lookback option

LambdaA measure of the effective leverage of aninstrument. It is defined as thepercentage change in the market value ofa derivative for a one-percent move in theunderlying. Unlike gearing, the lambdavalue captures the instrument’s delta.See also leverage

Lease rate swapSimilar to an interest rate swap, a leaserate swap is a fixed-for-floatingagreement in which gold is borrowed/lent at a "fixed" rate.The floating leg is re-priced at incremental time periodsover the maturity of the swap. At the endof each floating period the agreed uponbenchmark lease rate is compared to thecontract rate and the party in debit paysthe differential.The floating component is then rolled out for a further period.

Legal riskLegal risk arises from the risk of notlegally being able to enforce contracts. Itcan be a particular issue in emergingmarkets where derivatives regulations arestill being developed.

LeptokurtosisSee kurtosis

LeverageThe ability to control large amounts of anunderlying variable for a small initialinvestment. Futures and options areregarded as leveraged products because the initial premium paid by the purchaser is generally muchsmaller than the nominal amount of the underlying. Leverage is usuallymeasured as a quantity called lambda.See also lambda

Leveraged inverse floaterSee also inverse floater

LiborThe London inter-bank offered rate(LIBOR) is the interest rate charged onshort-term interbank loans by banksoperating in London.The rate is set on adaily basis and is commonly used as aguide for the future level of interest rates.

Libor-in-arrears swap See delayed reset swap

Limit binarySee range binary


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LLinear basket credit default swapA basket credit default swap, whereinvestors are exposed to multiplereference entities as if they had enteredinto a separate credit default swapcontract with respect to each reference entity.

Linear ex-linked swapAn interest rate swap with a quasi-fixedcoupon that varies with the movement ofa chosen spot foreign exchange rate overthe life of the deal.These swaps can bestructured to pay a higher (or lower)coupon if a given currency weakens (orstrengthens) after the outset of the deal.The observation dates for the forexcomponent coincide with the Libor reset dates for coupon calculation.Theseswaps can be structured with a leveragedforex exposure.

Liquidity riskThe risk associated with transactionsmade in illiquid markets. Such marketsare characterised by wide bid/offerspreads, lack of transparency and large movements in price after a deal ofany size. A firm wishing to unwind aportfolio of illiquid instruments (forexample, highly tailored structured notes)may find it has to sell them at prices farbelow their fair values, exacerbating the problems that prompted the decisionto unwind.

Listed option See warrant, option

Lite optionA European-style basket option with apayout determined by the underlyingassets that remain in the basket, after acertain number of the best and worstperforming assets in the basket wereremoved at a specified date prior toexpiry. Also known as an atlas option.

Local capA local cap is the maximum return in eachperiod of a cliquet option, which is usedto work out the overall payout.

Local floorA local floor is the minimum return ineach period of a cliquet option, which isused to help work out the overall payout.

Longstaff-Schwartz model A two-factor model of the term structureof interest rates. It produces a closed-formsolution for the price of zero couponbonds and a quasi-closed-form solutionfor options on zero coupon bonds.Themodel is developed in a Cox-Ingersoll-Ross framework with short interest ratesand their volatility as the two sources ofuncertainty in the equation.

Lookback optionLookback options give the holder theright at expiry to exercise the option atthe most favourable rate or price reachedby the underlying over the life of theoption. As with average options, the strikemay be either fixed or floating.With anoptimal rate (or price) lookback option,




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the strike is fixed at the outset and theoption will pay out against the highest (fora call) or lowest spot (for a put) reachedover the life of the option, irrespective ofthe spot at expiry.The option will usuallybe settled in cash. Since the option is likelyto have a larger payout than thecorresponding plain vanilla option, itcommands a larger premium.The strikefor an optimal strike lookback option, onthe other hand, is not fixed until expiry,when it is set to be the highest (for a put)or lowest spot (for a call) over the option’slife and exercised for cash or physicalagainst the spot prevailing at expiry. Seealso cliquet option, ladder option, path-dependent option, shout option

Low exercise price option (Lepo)A low exercise price option (Lepo) is a calloption with an exercise price set deep in-the-money.The limiting case, a zeroexercise price option, is when the strikeprice is zero. It is virtually certain to beexercised and the value and performanceof its intrinsic value is effectively identicalto that of the underlying equity.These features are designed to allowparticipation in the performance of anequity price where there are legal orfinancial obstacles to purchasing theunderlying directly. If the Lepo is cash-settled, the buyer profits to the sameextent as with a direct holding in theunderlying, but without having totransact in it. However, a Lepo holder doesnot earn dividends or have voting rightsover the equity.

MMandarin collarThe Mandarin collar combines a rangeforward with the purchase of a rangebinary structure, such that should thespot stay within the prescribed range, theproceeds of the range forward areenhanced by the payout amount of therange binary. If either of the limits tradesat any time, the range binary isterminated, but the underlying exposureremains hedged by the range forward.

Margrabe optionSee outperformance option

Market model of interest ratesA special case of the Heath-Jarrow-Morton model due to Brace, Gatarek andMusiela in which the term structure ofinterest rates is modelled in terms ofsimple Libor rates (which are lognormally distributed with respect to forward measure) rather thaninstantaneous forward rates.This allowsthe modeller to exclude the possibility of negative interest rates from the model and obtain prices for caps,floors and swaptions consistent with the Black-Scholes framework.The model can be calibrated using readilyavailable market data: forward or swaprates volatilities and correlations, and is particularly suited to path-dependent instruments.


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MMarket riskExposure to a change in the value ofsome market variable, such as interestrates or foreign exchange rates, equity orcommodity prices. For holders of aderivatives position, market risk may bepassed through from a change in thevalue of the underlying to the price of thederivatives, or may arise from othersources, such as implied volatility or time decay.

Market valueSee replacement cost

Mark-to-marketThis is the value of a financial instrumentaccording to current market rates.

MartingaleA probabilistic interpretation of thepayout of a ‘fair game.’The expected gain at any point in the future is equal to the actual gain now. See alsostochastic process

Mean reversion The phenomenon by which interest rates and volatility appear to move back to a long-run average level.Interest rates’ mean-reverting tendency is one explanation for thebehaviour of the term structure ofvolatility. Some interest rate modelsincorporate mean reversion, such asVasicek and Cox-Ingersoll-Ross, in which high interest rates tend to go down and low ones up.

Medium-term note (MTN)A medium-term note is a debt instrumentwith a maturity of between three andseven years, which may pay fixed orvariable coupons.These notes can beused to construct structured notes byembedding derivatives to createstructured coupons which appeal to investors.

Mid-Atlantic optionSee Bermudan option

Monte Carlo Simulation A method of determining the value of aderivative by simulating the evolution ofthe underlying variable(s) many timesover.The discounted average outcome ofthe simulation gives an approximation ofthe derivative’s value.This method maybe used to value complex derivatives,particularly path-dependent options, forwhich closed-form solutions have notbeen or cannot be found. Monte Carlosimulation can also be used to estimatethe value-at-risk (VaR) of a portfolio. Inthis case, a simulation of many correlatedmarket movements is generated for themarkets to which the portfolio is exposed,and the positions in the portfoliorevalued repeatedly in accordance withthe simulated scenarios.The result of thiscalculation will be a probabilitydistribution of portfolio gains and lossesfrom which the VaR can be determined.The principal difficulty with Monte CarloVaR analysis is that it can be verycomputationally intensive.




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Mortgage swap An asset swap attached to fixed-ratemortgage payments. Mortgage swapsallow investors to enjoy the flows from aportfolio of mortgages without taking amortgage asset on to their balance sheet.The principal reduces if and when theoutstanding mortgage principal reduces(which can occur if the mortgage holderpays off the mortgage or defaults). Suchswaps are complicated because althoughthe fixed-rate receiver receives a higherrate than on a normal swap, theamortisation of the principal is not just afunction of interest rates.The largestmortgage swap market is in the US; in1992 and 1993 prepayments acceleratedbecause of historically low interest rates.See also index amortising swap, reverseindex amortising swap

Mortgage-backed securitySee asset backed security

Moving strike option An option in which the strike is reset over time, such as an interest rate cap in which the strike is reset for thenext period at the current interest rateplus a pre-agreed spread. See also cliquet option

Multi-factor model Any model in which there are two ormore uncertain parameters in the optionprice (one-factor models incorporate onlyone cause of uncertainty: the futureprice). Multi-factor models are useful for

two main reasons. Firstly, they permitmore realistic modelling, particularly ofinterest rates, although they are verydifficult to compute. Secondly, multi-factor options (for example, spreadoptions) have several parameters, eachwith independent volatilities, and also thecorrelation between the underlyingsmust be dealt with separately.

Multiple strike optionSee outperformance option

Municipal swap A swap in which the floating paymentsare based on an index of tax-exempt USmunicipal bonds, such as J.J. Kenny.

NNaked option An option that is sold (bought) without holding the underlying orotherwise hedging.

Natural hedgeA natural hedge is the reduction infinancial risk that can arise from aninstitution’s normal operating procedures.For instance, a company that has asignificant portion of its sales in onecountry will have a natural hedge to atleast part of its currency risk if it also hasoperations in that country generatingexpenses in the currency. Firms may actto increase natural hedges by changing


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N/Osourcing, funding, or operationaldecisions, but natural hedges are lessflexible, and more difficult to reverse, thanfinancial hedges.

Negative basisNegative basis exists when the cost ofbuying protection (in the creditderivatives market) on a particularreference entity is less than the creditspread (generally expressed as a spreadto Libor) on a bond or note of similarmaturity issued by that reference entity.When this occurs, investors can lock inriskless profit by buying bonds andbuying credit protection.These arbitrage opportunities are generally only available to investors whose cost of funds is Libor flat or better (sincefunding the bond or note at Libor plus aspread will erode the arbitrage).Technical factors between the bond andcredit derivatives market account fornegative basis.

Net present valueA technique for assessing the worth of future payments by looking atthe present value of those futurecashflows discounted at today’s cost of capital.

Non-deliverable forwardNon-deliverable forward contracts(NDFs) – also called dollar-settledforwards – are synthetic forwards, whichentail no exchange of currencies atmaturity. Instead, settlement is made in

US dollars based on the differencebetween the agreed contract rate atinception and a market reference rate atmaturity. NDFs can be used to establish ahedge or take a position in one of agrowing group of emerging marketcurrencies where conventional forwardmarkets either do not exist or may beclosed to non-residents. As offshoreinstruments, NDFs offer the advantage ofeliminating convertibility risk, since noemerging market currencies areexchanged at maturity.

OOne-factor model A model or description of a system wherethe model incorporates only one variableor uncertainty: the future price.These aresimple models, usually leading to closed-form solutions, such as the Black-Scholesmodel or the Vasicek model.

Open-ended productStructured products that can be used forinvestment for an unlimited period aresometimes called open-ended products.They stand in contrast to tranche or close-ended products.

Operational riskThe risk run by a firm that its internalpractices, policies and systems are notrigorous or sophisticated enough to copewith untoward market conditions or




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human or technological errors. Althoughoperational risk is not as easy to identifyor quantify as market or credit risk, it hasbeen implicated as a major factor in manyof the highly-publicised derivatives lossesof recent years.

Sources of operational risk include:failure to correctly measure or report risk;lack of controls to prevent unauthorisedor inappropriate transactions being made(the so-called ‘rogue trader’ syndrome);and lack of understanding or awarenessamong key staff.

Option A contract that gives the purchaser theright, but not the obligation, to buy or sellan underlying at a certain price (theexercise, or strike price) on or before anagreed date (the exercise period).

For this right, the purchaser pays apremium to the seller.The seller (writer) ofan option has a duty to buy or sell at thestrike price, should the purchaser exercisehis right.With European-style options,purchasers may take delivery of theunderlying only at the end of the option’slife. American-style options may beexercised, for immediate delivery, at anytime over the life of the option. Holders ofsemi-American-style or Bermudanoptions may be exercised on specifieddates – typically on a monthly orquarterly basis.

Options can be bought oncommodities, stocks, stock indexes,interest rates, bonds, currencies, etc.Thetrading terminology, though, may change

according to the product. In most cases,the right to buy the underlying is knownas a call, and the right to sell, a put.

Options are traded on formalexchanges and in over-the-counter (OTC)markets.The exchanges, such as the HongKong Stock Exchange, the SIMEX, or theASX provide primarily standardisedoptions; the OTC markets are able toprovide tailored products to fit specificrequirements.The choice between OTCand exchange-traded options willdepend on the degree of tailoringrequired, the relative liquidity of bothmarkets (this varies greatly according tothe underlying) and credit concerns.

Pricing models for simple or vanillaoptions have five major inputs: theoption’s exercise or strike price; the timeto expiration; the price of the underlyinginstrument; the risk-free interest rate onthe underlying instrument, and thevolatility of the underlying instrument.

European-style options are usuallypriced off a closed-form analytical modelfirst published by Fischer Black andMyron Scholes in 1973, which hassubsequently been modified to fitdifferent underlying.

At maturity, an option’s value willdepend on the value of the right to buyor sell a product. If an option is purchasedgiving the right to buy gold at $375 anounce and at expiration the price is $400,the option is worth $25.

The extent to which an option is in-the-money (how far the strike price isbelow/above the current forward market


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Oprice) is called its intrinsic value.Wherethe strike price is less favourable than themarket price, the option is said to be out-of-the-money, and where the two pricesare the same it is at-the-money.

At any time before maturity, an option’sprice will be a combination of its intrinsicvalue (which is always either greater than,or equal to, zero) and its time value.Thelatter includes the cost of carry and theprobability that the price of the underlyingwill move into or remain in the money.Options can broadly be used in two ways –for speculation, or for insurance.Theirusefulness, both from a buyer’s and aseller’s point of view, derives from theirpayouts. In contrast to other types ofhedge, options provide insurance againstunfavourable moves in a product’s priceand the opportunity to take advantage offavourable moves. Forwards and futures,for example, require buyers and sellers tolock into one rate. In return for assumingthis risk, sellers of options receive apremium, effectively a risk-taking fee.The payout of a purchased option meansthat the price risk of an option is limitedto its premium – it is not as exposed toadverse movements as a position in the underlying.

For speculators selling (writing)options, this often means taking a nakedoption position and therefore beingexposed to adverse movements in theunderlying. Hedgers may sell options togarner premium to offset any expectedslight downturn in a market. Since optionpremiums are only a fraction of the cost

of the underlying product, it is possible toachieve a much greater exposure to pricechanges of the underlying comparedwith a similar investment directly in theproduct – this is called leverage. See alsoimplied volatility

Option combination strategies Options may be combined so that theirpayouts produce a desired risk profile.Some combinations are primarily tradingstrategies, but option combinations canbe useful in, for example, allowinginvestors to construct a strategy to takeadvantage of a particular view they haveof the market. Other strategies allowpurchasers to reduce their premiums bygiving up some of the benefits they mayhave received from market movements.See also put spread, straddle, strangle

Option on future See futures option

Option replicationSee replication

Option stylesThe purchaser of a European-style optionhas the right to exercise it on apredetermined expiry date. In contrast, theholder of an American-style option has theright to exercise it at any time during itslifetime, up to and including its expiry date.This flexibility means there is a greaterprobability of an American-style optionbeing exercised than the correspondingEuropean-style option with the same




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strike. Hence the early exercise feature ofan American option adds value and makesit the more expensive of the two. Mostexchange-traded options are American-style. Further variations on these styles alsoexist. A Bermudan option, so calledbecause it falls between American- andEuropean-style options, has more than onepossible exercise date. For example, theholder of a Bermudan option with a two-year maturity might have the right toexercise it every quarter or half year duringthe life of the contract. Bermudans are alsoknown as limited exercise or semi-American-style options. Another twist isthe deferred payout option, a variation onAmerican-style options in which theoption can be exercised at any time duringthe option’s life, but the payout is delayeduntil the expiry date.With the similar shoutoption, the purchaser can lock in a profit atany time, but retains the right to profitfrom further favourable moves. See alsoAmerican-style option, Bermudan option,deferred payout option

Out-of-the-money Describes an option for which theforward market price of the underlying isbelow the strike price in the case of a call,or above it in the case of a put. The morethe option is out-of-the-money, thecheaper it is (since the chances of itbeing exercised get slimmer). Its deltaalso declines and it becomes lesssensitive to movements in theunderlying. See also at-the-money, in-the-money

Outperformance optionAlso known as a Margrabe option. A two-factor option giving the purchaser theright to receive the outperformance ofone asset over another asset. Forexample, a purchaser with a view thatthe Hang Seng Index (HSI) willoutperform the Dow Jones Euro Stoxx 50(Euro Stoxx) index should buy theoutperformance option, which paysnotional multiplied by theoutperformance of the HSI index overthe Euro Stoxx index. In this case, thepayout is zero if HSI underperforms Euro Stoxx. The value of anoutperformance option will largely bedictated by the historical correlationbetween the underlyings.

Overlay A strategy to change the exposure of aportfolio using derivatives, while leavingthe securities in the underlying portfoliounchanged. This has the advantage ofcost and flexibility, as portfolio managers can adjust portfolio risk more quickly and cheaply withderivatives than by liquidating portfolioholdings. Another reason might betactical – the adjustment may only bedesired for a brief period of perceivedmarket threat. A third reason might be to transform a portfolio risk; aninternational fund manager may wish tosegregate the currency aspect of aportfolio and can do so with a currency overlay programme. See alsoasset allocation


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O/POver-the-counter (OTC)Financial products that are not traded onformal exchanges are said to be tradedover-the-counter.

PParisian barrier optionA barrier option with a barrier that is triggered only if the underlying has beenbeyond the barrier level for longer than aspecified period of time. See also barrier option, trigger, trigger condition

Participating forward The simultaneous purchase of a calloption (put option) and sale of a put (call)at the same strike price, usually for zerocost.The option purchased must be out-of-the-money and the option sold (tofinance the option purchase) is for asmaller amount and will be in-the-money.See also zero cost option

Participating optionAn option whereby the buyer pays areduced premium but has to forgo aportion of his potential gains.

Participating swap A swap in which floating-rate exposure ishedged but in which the hedger stillretains some benefit from a fall in rates.

Participation rateMany structured products incorporate

returns at maturity that are calculated bymultiplying the performance of theunderlying (which can be an index, stockbasket or fund) by a fixed percentage.Thispercentage is called the participation rate.For example, a 70% participation in theindex means that 70% of the performanceof the underlying index will be used tocalculate the maturity payout. If theproduct comes with a 100% capitalguarantee, the participation rate will onlyapply to the upside, not to index losses.

Path-dependent option A path-dependent option has a payoutdirectly related to movements in the priceof the underlying during the option’s life.By contrast, the payout of a standardEuropean-style option is determinedsolely by the price at expiry. See alsobarrier option, cliquet option, high-lowoption, lookback option, shout option

Pay-as-you-go capA pay-as-you-go cap allows the buyer topay for protection from upward moves inan interest rate for only as long asnecessary. Usually, the holder will pay aninitial premium (which will be smallcompared with the premium for a normalcap) and a further payment at each resetdate.The holder can cancel the cap whenhe or she feels that the protection is nolonger needed. A pay-as-you-go cap isuseful for those who feel that caps are tooexpensive, that interest rates willeventually stabilise below the cappedlevel, or that rates are in a short-lived




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‘spike’ move. Also known as aninstallment cap.

Payout/payoffA general term used to describe thereturn provided by a structured productor an option. A lot of products pay a fixedcoupon plus additional returns linked toperformance of the underlying. If theembedded option is path-dependent, thereturns will be a function of both theperformance of the index and the payoutformula. For example, the payout from afive-year quarterly Asian option with a70% participation of the Dow Jones EuroStoxx 50 Index is equal to 70% of theaverage of 20 different prices over fiveyears, and not the level of the index at maturity.

Period resetting swapAn interest rate swap in which thefloating-rate payments are an average ofthe floating rates observed since the last payment.

Periodic cap A cap in which the strike rate can varyfrom period to period.The strike rate in agiven period depends upon the strike setin the previous period. Such caps arenormally set at a fixed number of basispoints above the previous strike, or theindex (for example, Libor) plus a spread.Periodic caps can be with or without"memory". A periodic cap withoutmemory simply looks at the strike in theimmediately preceding period to

determine a new strike, while one withmemory may look at previous settings indetermining the new strike. Periodic capsare common features in adjustable ratemortgages (ARMs) in the US where theborrower’s floating interest paymentscannot go up by more than a set numberof basis points in a given year. See alsoperiodic floor

Periodic floor A floor in which the strike rate can varyfrom period to period.The strike rate in agiven period depends upon the strike setin the previous period. Such floors arenormally set at a fixed number of basispoints above the previous strike or theindex (for example Libor) plus a spread.See also periodic cap

Pin riskThe phenomenon where a small move in the underlying can have a significantimpact on the value of an at-the-moneyoption shortly before expiration.

PodiumA type of correlation product that is fullycapital-guaranteed, but with the annualcoupons dependent upon the number ofunderlyings within the basket that meetcertain performance criteria.

Portfolio optionA portfolio option is a multi-factor optionthat pays out the difference between thereturn from a portfolio of assets and aspecified strike price.


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PPositive basisPositive basis exists when the cost ofbuying protection (in the creditderivatives market) on a particularreference entity exceeds the credit spread(generally expressed as a spread to Libor)on a bond or note of similar maturityissued by that reference entity.When thisoccurs, investors looking to gain exposureto the reference entity can improve theirexpected return on an investment bytaking exposure to the credit by sellingprotection in the credit derivativesmarket rather than buying the bond ornote.Technical factors between the bondand credit derivatives market account forpositive basis.

Power optionAn option with a payout dependent onthe price of the underlying at expiry,raised to some power. See also power swap

Power swapA swap whose floating leg is based on thesquare (or some higher exponent) of thereference interest rate. Althoughdismissed by some as little more than aspeculative tool for taking highlyleveraged positions on the direction ofinterest rates, power swaps have beenshown (by Robert Jarrow and Donald vanDeventer) to have their uses in hedgingcommercial banks’ deposits and creditcard loan portfolios. See also power option

Premium See option

Premium-reduction deviceA strategy that aims to reduce the cost ofan option or other derivative.There aremany ways to achieve this; three commontechniques follow.

The first is to sell a second derivative;the premium received can then be usedto lower the funding requirement for thepurchased derivative.This is thetechnique employed for reducing thecost of a collar.

The second is to limit participation inmoves in the underlying by imposinglimitations on the payout profile of theinstrument (as in a barrier option or acapped floater).

The final way is to accept paymentsbelow market rates, with the possibility ofmaking up the shortfall at the end of theinstrument’s life (see yield adjustment).

Principal-guaranteed productAny investment vehicle that allowsinvestors to gain exposure to an assetwhile guaranteeing the return of theirprincipal, often at maturity only. Suchproducts are normally constructed bybuying a deep discount bond (often azero-coupon bond) and using the rest ofthe money to buy embedded call or putoptions to gain exposure to a secondasset, often a stock index. See alsoguaranteed return on investment

Program trading A strategy to trade a basket of sharessimultaneously, normally by means ofcomputer-generated instructions.Where




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the asset class is considered moreimportant than the selection within thatclass, program trading (also known asbasket trading) is used to lower tradingcosts since trading a basket of shares ischeaper than buying or selling thoseshares individually. Program trading isdifferent from stock index arbitrage,although it is used in such a strategy.

PromptFor immediate (ie, two days) delivery.

Protection levelThis refers to the safety level of theunderlying at which the investor can stillkeep their capital intact. Once this level isbreached, the original investmentamount is at risk.

Put option See option

Put spread A put spread reduces the cost of buying aput option by selling another put at alower level.This limits the amount thepurchaser can gain if the underlying goesdown, but the premium received fromselling an out-of-the money put partlyfinances the at-the-money put. A putspread may also be useful if the purchaserthinks there is only limited downside inthe market. See also call spread, optioncombination strategies

Put-call parity The relationship between a European-

style put option and a European-style calloption on the same underlying with thesame exercise price and maturity. Put-callparity states that the payout profile of aportfolio containing an asset plus a putoption is identical to that of a portfoliocontaining a call option of the same strikeon that same asset (with the rest of themoney earning the risk-free rate ofreturn). In practice, a put option on, say, astock index, can be constructed byshorting the stock and buying a calloption.The relationship means thattraders are able to arbitrage mispricedoptions. See also reversal

Puttable swap An interest rate swap in which the fixed-rate payer has the right to terminate thecontract after a specified period. Shouldinterest rates fall, the swap can thus beput back to the fixed receiver.Theputtable swap is the opposite of acallable swap.The fixed-rate payer iseffectively sold a swaption by thefloating-rate payer, who receives a higherfixed rate in compensation. Puttableswaps are similar to extendible swaps.Also known as a cancellable swap.

QQuanto product An asset or liability denominated in acurrency other than that in which it is


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Q/Rusually traded, typically equity indexfutures, equity index options, bondoptions and interest rate swaps(differential swaps). Quanto products canbe hedged with an offsetting position in alocal currency product.Variable asset andforeign exchange exposures will arisewith changes in the foreign exchangerate and in the underlying, so thestructures must be continuallydynamically hedged in a similar fashionto option products. See also guaranteedexchange rate option, joint option

Quanto swapAlso called a differential swap. A quantoswap is a fixed-floating or floating-floatinginterest rate swap. One of the floating ratesis a foreign interest rate, but is applied to anotional amount denominated in thedomestic currency. For example, a USinvestor may enter into a five-year swap inwhich he makes payments in US dollars atthe six-month USD Libor plus a spreadsemi-annually, and receives payments inUS dollar at JPY Libor.The payments arecalculated by applying the respectiveinterest rates to a notional amount ofUS$100 million. However, the notionalprincipal can also be denominated in theJapanese yen, or in a third currency such asthe British pound. A quanto swap enablesthe investor to avoid exchange rate riskwhile taking advantage of interest ratedifferentials. A corporate borrower withdebt in a discount currency can use aquanto swap to lower his borrowing costs,while portfolio managers can use a quanto

swap to enhance yield with higher interestrates in a discount currency.

RRainbow optionSimilar to a multi-factor option. It is anoption with the payout linked to two ormore underlying instruments or indexes.Some common types of rainbow optionsare the maximum option, minimumoption, best-of option and worst-ofoption.The underlyings are of the sameasset class and can have different expirydates and strike prices, but for the option to payout, all the underlyings must move in the direction that isfavourable to the option holder. However,if the option combines two or more types of asset classes, such as a stockindex and an exchange rate, it is called a hybrid option.

Random walkThe series of values taken by a randomvariable with the progress of someparameter such as time. Each new value(each new step in the walk) is selectedrandomly and describes the path takenby the underlying variable.See also stochastic process

Range accrual optionAn option that pays out a fixed amount atexpiration for each day that the index rateremains within the specified range.




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Range binaryThe range binary structure has beendeveloped primarily for trading purposesand is essentially a bet on a spot stayingwithin a given range.The strategy is oftenlinked with a deposit for yieldenhancement purposes.

A range is specified by the customerover a fixed period. A premium is paid upfront and provided that the spot stayswithin the range (as monitored on a 24-hour basis), then a multiple of thepremium invested will be payable.A rebate range binary is one in which thepremium invested is rebated if adesignated boundary of the range isbreached first. A similar structure, the limitbinary, is also essentially for trading.This isfundamentally a bet on a spot not stayingwithin a predetermined range.Thecustomer specifies two spot rates, oneabove and one below the current spotrate. A premium is paid up front, andproviding that both levels trade (asmonitored on a 24-hour basis), a fixedmultiple of the premium invested will bepayable. See also trigger condition

Range noteA range note (also known as a fairwaynote, an accrual note, or a corridor floater)is a structured note, which pays a couponfor each day that the underlying spotstays within a specified range (sometimescalled the accrual corridor). If theunderlying trades outside the specifiedrange, the investor receives no interest forthat day.The underlying can be a

reference interest rate, a foreignexchange rate, an equity price or thespread between two interest rates.Therange is determined at the outset to suitthe investor’s risk/return requirements,but might also be reset by the investor orbe automatically centred on theprevailing rate at each reset date.Thishigher yield is achieved by the investorselling an embedded corridor option,particularly in times of high volatility.Theholder of the note will therefore benefitin stable market periods when volatility is low.

Range resettable forwardA type of forward contract that offers amore favourable forward rate comparedwith an ordinary forward, as long as the spot rate remains within a pre-defined range.

Ratchet floaterAlso called a one-way floating rate note. Aratchet floater is a structured note thatpays a floating interest rate indexed on areference rate such as Libor. Each floatinginterest rate will depend on the previousinterest rate paid.

Ratchet optionSee cliquet option

Ratio calendar spreadA strategy that involves the purchase of along-term option (either call or put) andthe selling of a greater amount of near-term option at the same strike price.


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RRebateBarrier options often have a rebateassociated with the trigger level(s). Arebate is an amount paid to the holder ofthe derivative if the instrument isknocked-out or is never activated duringits lifetime as partial recompense for theirinitial investment. One example is therebate range binary.

Regulatory arbitrageA financial transaction that allows one orboth of the counterparties to accomplishan operating or financial objective thatwould be unavailable to them directlybecause of regulations: for example, acommercial bank entering into a creditdefault swap with an OECD bank in orderto lower the regulatory capital that itmust hold.

Regulatory capital The amount of capital that an organisationis required to hold by its regulator.

Reinvestment riskThe risk that an asset manager will beunable to match the yield from aninterest-rate instrument (such as a swapor bond) when reinvesting its couponpayments and principal repayments.

Relative performance optionSee outperformance option

Relative performance riskThe risk that a fund manager’s choice ofinvestments will fail to match the

performance of the benchmark againstwhich the fund is measured, promptingfund redemptions. A similar risk is run bycorporate treasury risk managers who aremeasured against benchmark hedgelevels. One way to address this type of riskis with outperformance options. Relativeperformance risk is also used to refer tothe risk that an individual asset willunderperform relative to its asset class.For equities, this may be measured by astock’s beta, its standardised covariancewith respect to the relevant equity index.See also specific risk

Replacement costOften used in terms of credit exposure,the replacement cost of a financialinstrument is its current value in themarket – in other words, what it wouldcost to replace a given contract if thecounterparty to the contract defaulted.Aside from bid-ask conventions, it issynonymous with market value.

ReplicationTo replicate the payout of an option bybuying or selling other instruments.Creating a synthetic option in this way isalways possible in a complete market. Inthe case of dynamic replication thisinvolves dynamically buying or sellingthe underlying (or normally, because ofcheaper transaction costs, futures) inproportion to an option’s delta. In thecase of static replication the option(usually an exotic option) is hedged with a basket of standard




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options whose composition does notchange with time – eg, an at-expirydigital option can be replicated with acall spread. See also static replication,synthetic asset

Repo agreement To buy (sell) a security while at the sametime agreeing to sell (buy) the samesecurity at a predetermined future date.The price at which the reverse transactiontakes place sets the interest rate over theperiod (the repo rate).The most activerepo market is in the US, where theFederal Reserve sets short-term interestrates by lending securities. In a reverserepo the buyer sells cash in exchange for asecurity. Repos can benefit both parties.Buyers of repos often receive a betterreturn than that available on equivalentmoney-market instruments; and financialinstitutions, particularly dealers, are ableto get sub-Libor funding. A slight variationon the repo is the buy/sell back.Thebuy/sell back’s coupon becomes theproperty of the purchaser for the durationof the agreement. It is preferred by credit-sensitive investors such as central banks.

Repo rate See repo agreement

Reset-in-arrears swapSee delayed reset swap

Resettable convertible bond It is a convertible bond where theconversion ratio can reset to a new value

depending on the average price of theunderlying stock on pre-specified dates.See also convertible bond

Reversal To take advantage of mispriced optionsby creating a synthetic long futuresposition and hedging it by selling futurescontracts against it. A trader may buy anundervalued call, at the same time sellinga fairly valued put and buying a futurescontract.The same strategy could beapplied if the put was undervalued.The ability to undertake this risklessarbitrage relies on put-call parity. See alsoconvergence trade, put-call parity

Reverse barrier optionSee barrier option

Reverse cash-and-carry arbitrage A technique, used mainly in bond futuresand stock index futures, that involvesbuying a futures contract and selling theunderlying. It is used when a futurescontract is theoretically cheap, such aswhen the implied repo rate is less thanthe market repo rate. See also cash-and-carry arbitrage

Reverse convertibleThese are just like convertible bonds.Themain difference is that rather than buyinga call option on a stock, the investor sellsa put on the stock or index.The investorreceives higher than normal coupons butmay lose some principal if the put endsup in the money.


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RReverse index amortising swap An interest rate swap in which paymentsare linked to an index (eg, Libor orconstant maturity Treasuries) andincrease if that index declines.The swaptherefore exhibits positive convexity.Receiving fixed in a reverse indexamortising swap (reverse IAS) provides ahedge for instruments (such as mortgageswaps) that amortise as interest ratesdecline, although it is important to ensurethat the indexes on which theamortisation or accreting schedules arebased are highly correlated. Unlike aconventional IAS, the fixed receiver of areverse IAS is buying volatility (sometimesreferred to as ‘optionality’) which offsetsthe short option position of a mortgageportfolio. See also mortgage swap

Reversible swap An interest rate swap in which one sidehas an option to alter the payment basis(fixed/floating) after a certain period.Thisis usually achieved by the use of aswaption, allowing the purchaser theopportunity to enter a swap with paymenton the opposite basis.The swaptionwould be for twice the principal amount,one half nullifying the original swap.

Rho Measures an option’s sensitivity to achange in interest rates.This will have animpact on both the future price of theoption and the time value of thepremium. Its impact increases with thematurity of the option.

Risk neutral valuation An argument that underpins mostderivatives pricing, including the Black-Scholes model.The differential equationdescribing the price of a derivative doesnot involve parameters that depend onrisk preferences. Derivatives prices in amarket where all investors are risk neutralmust therefore be the same as prices in thereal world and this corollary considerablysimplifies model construction.

Risk reversalThe term ‘risk reversal’ is also used, bycurrency option traders, to denote thedifference in implied volatility betweenout-of-the-money call and put options,which both have a delta of 25%.The levelof the risk reversal is often used as asentiment indicator in currency markets as it indicates the relativedemand for calls versus puts. See alsocollar, volatility skew

Roller-coaster swapAn interest rate swap in which onecounterparty alternates between payingfixed and paying floating. Another namefor a seasonal swap.

Roll-over riskThe risk that a derivatives hedge positionwill be at a loss at expiry, necessitating acash payment when the expiring hedge isreplaced with a new one. Normally, such aroll-over loss simply represents anopportunity loss, but sometimes the cashcost is consequential.




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SSeasonal swap An interest rate swap in which theprincipal alternates between zero and the notional amount (which canchange or stay constant).The principalamount of the swap is designed to hedge the seasonal borrowing needs of a company.

SecuritisationThe conversion of assets (usually forms ofdebt) into securities, which can be tradedmore freely and cheaply than theunderlying assets and generate betterreturns than if the assets were used ascollateral for a loan. One example is themortgage-backed security, which poolsilliquid individual mortgages into a singletradable asset.

Semi-fixed swap An interest rate swap with two possiblefixed rates, which can be tailored to suitbullish or bearish market views.The ratepaid by the fixed-rate payer depends onwhether current Libor (or anotherreference rate or asset) is above or belowa predetermined level. In a typicalstructure, if Libor is below the triggerlevel, the lower of the two rates is paid, ifit is above, the higher is paid.These swapscan be used to create asymmetric riskexposures, ie, cheaper fixed-rate fundingfor an oil producer when oil prices are

low, or an enhanced yield for an insurancecompany when equity prices are falling.

Settlement riskSettlement risk (delivery risk), as aparticular form of counterparty credit risk,arises from a non-simultaneous exchangeof payments. For example, a bank thatmakes a payment to a counterparty, butwill not be recompensed until a laterdate, is exposed to the risk that thecounterparty may default before makingthe counter-payment. Settlement risk isdistinct from market risk because itrelates to exposure to a counterpartyrather than exposure to the underlyingrisk related to the reference entity of thederivatives contract.

Shout optionA type of path-dependent option thatallows the investor to lock in profits if hethinks the market has reached a high (fora call) or low (for a put).The investorbenefits further if the market finisheshigher or lower than the shout level.Theshout option is designed for investorswho have a directional view on themarket and want to take positions, butare worried about the volatility of theasset and want to lock in a minimumreturn. See also lookback option, path-dependent option

SkewA skewed distribution is one that isasymmetric. Skew is a measure of thisasymmetry. A perfectly symmetrical


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Sdistribution has zero skew, whereas adistribution with positive (negative) skewis one where outliers above (below) themean are more probable. An example ofan asymmetric distribution in thefinancial markets is the distributionimplied by the presence of a volatilityskew between out-of-the-money call andput options.

Specific riskSpecific risk, also known as non-systematic risk, represents the pricevariability of a security that is due tofactors unique to that security, asopposed to that portion that is due tosystematic risk, the generalised pricevariability of the related interest rate orequity market. As an example, a USTreasury note would have no specific risk,as it is deemed to have no risk other thanmovement in interest rates, while acorporate bond would have a degree ofdefault risk as well as more generalisedyield curve risk. See also relativeperformance risk

Spread optionThe underlying for a spread option is theprice differential between two assets (adifference option) or the same asset atdifferent times or places. An example of afinancial difference option is the creditspread option, the underlying for which isthe spread between two debt issues,which derives from the relative creditrating of the issuers. Another is the cross-currency cap, where the underlying is the

spread between interest rates in twodifferent currencies. A calendar spread, apair of options with the same strike pricebut different maturities, pays out theprice difference for a single asset on twodifferent dates. Spread options, includingcalendar spreads, are particularly popularin the commodity markets.

Spread-lock swap An interest rate swap in which onepayment stream is referenced at a fixedspread over a benchmark rate such as US Treasuries.

SqueezePressure on a particular delivery dateresulting in making the price of that datehigher relative to other delivery dates.

Static replicationStatic replication is a method of hedgingan options position with a position instandard options whose compositiondoes not change through time.Themethod attempts to replicate the payoutof the instrument in a more manageablefashion than dynamic replication, where aposition in the underlying or futurescontracts must be dynamically adjusted ifit is to remain effective. Because it usesoptions to hedge options, a staticreplication portfolio is a better hedge forgamma and volatility, as well as delta,than dynamic replication. Staticreplication can be used for hedging aposition in exotic options with vanillaoptions, or for replicating a long-term




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option with short-term options. Inpractice, however, it is not always possibleto hedge using static replication.Thenumber of different options and notionalamounts required can quickly becomeunmanageable. See also delta-hedging,replication, synthetic asset

Statistical arbitrageIn the mid-1980s it was discovered thatcertain stock prices did to an extentexhibit autocorrelations – implying thatearlier price changes could be used toforecast future changes. Statisticalarbitrageurs seek to exploit thesepatterns in their trading strategies.

Step-down swapThe opposite of an escalating rate swap;ie, the fixed rate decreases in incrementsover the life of the swap

Step-up swapSee accreting

Step-up/down range forwardA self-adjusting range forward structure,which is particularly suitable for hedgingpurposes. If the strike level of the long put option is breached, the strikeautomatically adjusts up or down(according to exposure) to a new, morefavourable, level.

Stochastic optimisation model A model or description of a system inwhich the choice of action that can betaken is dependent on the values of some

random variables. For example, the valueof an American-style option is such thatthe best choice of exercise is always made.

Stochastic processFormally, a process that can be describedby the evolution of some random variableover some parameter, which may beeither discrete or continuous. GeometricBrownian motion is an example of astochastic process parameterised by time.Stochastic processes are used in financeto develop models of the future price ofan instrument in terms of the spot priceand some random variable; oranalogously, the future value of aninterest or foreign exchange rate. See alsoGeometric Brownian motion, martingale,random walk

Stochastic volatilityOne of the key assumptions of the Black-Scholes model is that the stockprice follows geometric Brownian motion with constant volatility andinterest rates. However, in real markets, volatility is far from constant.If volatility is assumed to be driven by some stochastic process, however,the Black-Scholes model no longerdescribes a complete market, since there is now another source ofuncertainty in the option pricing model. A variety of approaches have been attempted to resolve thisdifficulty since the mid-1980s, mostnotably the Heath-Jarrow-Mortonframework.


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SStock index arbitrage The technique of selling a futures contracton a stock index and buying theunderlying stocks, via programme trading,or vice versa when the price of the futurescontract is above or below its theoreticalvalue.The ability to conduct suchstrategies depends on the efficiency ofthe futures and cash markets.

Stock index future A futures contract on a stock index. Mostare cash-settled.The theoretical price of astock index future equals the cost ofcarrying the underlying stock for thatperiod: the opportunity cost of the fundsinvested minus any dividends. If the costof buying and holding the underlyingstocks is less than the futures price, anarbitrageur can sell futures and buy theunderlying stocks.

The higher interest rates are(compared with the dividend yield), thegreater the opportunity cost of holdingthe stocks, hence the futures price shouldbe higher than the current index price. Ifinterest rates are less than the dividendyield, the opportunity cost of holdingstocks is less and the futures price shouldfall below the current index price.There isusually a so-called arbitrage band inwhich, although the futures andunderlying prices diverge, it is notworthwhile arbitraging the two.Thisarises as a result of transaction costs frombid-ask spreads, the market impact ofbuying and selling stock, and execution risks.

Stock index option An option, either exchange-traded orover-the-counter, on a stock index.

Stock option An option, either exchange-traded orover-the-counter, on an individual equity.

Straddle The sale or purchase of a put option and acall option, with the same strike price, onthe same underlying and with the sameexpiry.The strike is normally set at-the-money.The purchaser benefits, in returnfor paying two premiums, if theunderlying moves enough either way. It isa way of taking advantage of an expectedupturn in volatility. Sellers of straddlesassume unlimited risk but benefit if theunderlying does not move. Straddles areprimarily trading instruments. See alsooption combination strategies

Strangle 11.. As with a straddle, the sale or purchaseof a put option and a call option on thesame instrument, with the same expiry,but at strike prices that are out-of-the-money.The strangle costs less than thestraddle because both options are out-of-the-money, but profits are only generatedif the underlying moves dramatically, andthe break-even is worse than for astraddle. Sellers of strangles make moneyin the range between the two strikeprices, but lose if the price moves outsidethe break-even range (the strike pricesplus the premium received).




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22.. The term strangle is also used, bycurrency option traders, to denote theaverage difference in implied volatilitybetween out-of-the-money call and putoptions with a 25% delta and the impliedvolatility of at-the-money forward options.See also option combination strategies

StrapA strategy that involves purchasing oneput option and two call options, all withthe exact same strike price, underlyingsand maturity date.

Strategic asset allocationThe distribution of investment funds inresponse to long-term, fundamentalexpectations for markets.

Stress-testingTo perform a stress test on a derivativesposition is to stimulate an extrememarket event and examine its behaviourunder the ‘stress’ of that event.

StripA strategy that involves the purchase ofone call option and two put options, allwith the same strike price on the sameunderlying and the same expiry date.Thestrikes are set at-the-money. Alternatively, astrip can refer to the process of removingcoupons from a bond and selling thestripped bond (or zero coupon bond) andinterest-paying coupons separately.

Structured productA structured product is an investment

that bundles up a portfolio of securitiesand other derivatives to create a single product. For example, a structured note can be a five-year bondthat has an embedded equity or currency option in order to enhance itsreturn. A structured product appeals tothe investor who has a view on themarket and a good idea of what hisrisk/reward appetite is.

Structured yield investmentsAny security (normally a structured note)whose yield is conditional on certaintrigger conditions being met. Such asecurity is normally constructed byembedding path-dependent options(such as binary options) in a vanilla debtissue.The investor’s return on the notewill then vary according to the payout ofthe options.

Substitution optionA bilateral financial contract in whichone party buys the right to substitute aspecified asset or one of a specifiedgroup of assets for another asset at apoint in time or contingent upon a credit event.

Swap See accreting, credit default swap, delayed reset swap, digital swap, dualcurrency swap, equity (index) swap, forward swap, high-coupon swap, indexamortising swap, interest rate swap,mortgage swap, municipal swap,participating swap, periodic resetting


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Sswap, power swap, puttable swap, reverseindex amortising swap, reversible swap,roller-coaster swap, seasonal swap, semi-fixed swap, spread-lock swap, step-down swap, variable notional swap,yield curve swap, zero coupon swap

SwaptionAn option to enter an interest rate swap.A payer swaption gives the purchaser theright to pay fixed, a receiver swaptiongives the purchaser the right to receivefixed (pay floating).

Apart from those in the sterlingmarket, many swaptions are capital-market driven. Good-quality borrowersare able to issue puttable or callablebonds and use the swaptions market toreduce their financing costs. In the case ofcallable bonds, the issuer effectively buysan option from the investor in return for aslightly higher coupon, so that it maybenefit if rates decline. Because many ofthese embedded options havetraditionally been underpriced, good-quality borrowers have been able tomonetise this anomaly by selling anequivalent swaption (a receiver swaption)to a bank at market rates.

The profit from this arbitrage lowersfunding costs. If the swaption is exercisedagainst the issuer, it calls the bonds(although the issuer would almostcertainly have called the issue given thereduction in rates). In the case of puttablebonds, the borrower sells a swaption tothe swaption market.The premiumgained lowers the funding cost at the

expense of leaving the borrower unsureof the maturity of the debt.

Synthetic assetA synthetic asset is a combination of longand short positions in financialinstruments, which has the samerisk/reward profile as another instrument.For example, it is possible to replicate thepayout and exposure of a short futuresposition by going short European-stylecall options and long European puts withidentical strikes and expiries. Syntheticindex options can be generated eitherthrough positions in the underlying andfutures contracts, or with a basket ofvanilla options. See also replication, static replication

Synthetic collateralised debt obligationA synthetic collateralised debt obligation(CDO) uses credit derivatives to transfercredit risk in a portfolio.This is in contrastto a traditional CDO, which is typicallystructured as a securitisation withownership of the assets transferred to aseparate special purpose vehicle (SPV).The assets are funded with the proceedsof debt and equity issued by the vehicle.In a synthetic CDO, an institution transfersthe total return or default risk of areference portfolio via a credit defaultswap, a total return swap, or a credit-linked note.The SPV then issues securitieswith repayment contingent upon the losson the portfolio. Proceeds are either heldby the vehicle and invested in highlyrated, liquid collateral, or passed-on to the




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institution as an investment in a credit-linked note. Balance sheet synthetic CDOsare typically used by banks to managerisk capital and are easier to execute thantraditional CDOs. Arbitrage syntheticCDOs are often used by insurancecompanies and asset managers and exploit the spread between the yield on the underlying assets and the reduced expense of servicing a CDO structure. See also collateralised debt obligation

Synthetic forwardSee synthetic asset

Synthetic optionSee synthetic asset, replication

Synthetic securitisationA first-loss basket swap structure thatreferences a portfolio of bonds, loans orother financial instruments held on afirm’s balance sheet.The techniquereplicates the credit risk transfer benefitsof a traditional cash securitisation whileretaining the assets on balance sheet.Advantages over cash securitisationinclude reduced cost, ease of executionand retention of on-balance sheetfunding advantage.

Systemic riskThe risk that the financial system as awhole may not withstand the effects of amarket crisis. Concern on the part ofbanking regulators has been caused bythe concentration of derivative risk among

a relatively small number of marketparticipants, with the concomitant riskthat the failure of a major dealer couldhave serious knock-on effects for manyother market participants.

TTable topSimilar to a ratio spread, except that thepurchase of an option is financed bysales of the same option at two differentstrike prices.

Tactical asset allocationThe distribution of investment funds inresponse to short-term expectations ofmarket opportunity or threat.

Theta This measures the effect on an option’sprice of a one-day decrease in the time toexpiration.The more the market andstrike prices diverge, the less effect thetahas on a vanilla option’s price.Theta isalso non-linear for vanilla options,meaning that its value decreases faster asthe option is closer to maturity. Positivegamma is generally associated withnegative theta and vice versa.

Time decay See theta

Time value The value of an option, other than its


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Tintrinsic value.The time value thereforeincludes cost of carry and the probabilitythat the option will be exercised (which inturn depends on its volatility).

Total return swapA bilateral financial contract in whichone party (the total return payer) makesfloating payments to the other party(the total return receiver) equal to thetotal return on a specified asset or index(including interest or dividend paymentsand net price appreciation) in exchangefor amounts that generally equal thetotal return payer’s cost of holding thespecified asset on its balance sheet.Price appreciation or depreciation may be calculated and exchanged atmaturity or on an interim basis. A total(rate of ) return swap is a form of creditderivative, but is distinct from a creditdefault swap in that floating paymentsare based on the total economicperformance of a specified asset and arenot contingent upon the occurrence of acredit event.

Total return optionA total return option is a put option ondebt. An investor that has a riskycorporate bond and is worried aboutdefault can buy a total return option thatallows him to sell the bond at par if thecorporation defaults.

Tracking errorRefers to the difference between theperformance of a portfolio of stocks and a

broad-based index with which they arebeing compared.

Tranche productA tranche product is one that is open for subscription for only a limited period, as opposed to open-ended products, which acceptinvestments for an unlimited period.Most structured products are tranche products, and the offer period isusually four to eight weeks.

Translation risk An accounting/financial reporting risk where the earnings of a company can be adversely affected due to its method of accounting forforeign operations.

Treasury lock A rate agreement based on the yield orequivalent market price of a reference USTreasury security.These can be settled based on yield differential for a full tenor, or can be price-settled based on the exact characteristics of aspecific security.

TriggerMany path-dependent options havepayouts that depend on the underlyingasset or index or coupons paid/payablereaching a specified level before theexpiry date. This level is the trigger. Someoptions have more than one triggerlevel, in which case the payouts areconditional or increase with the number




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of triggers activated or the order inwhich they are activated. See barrieroption, Parisian barrier option

Trigger conditionPath-dependent derivatives such asbarrier options and binary options havepayouts which depend in some way on amarket variable satisfying a specificcondition during the derivative’s life. Ifthis ‘trigger condition’ is met, thederivative may pay out immediately (earlyexercise) or at some other specified time(such as expiry). Alternatively, the optionmay only become effective (be knocked-in) or be de-activated (knocked out) whenthe trigger condition is met.

The most common condition is thatthe spot rate or price of the underlyingmust breach a specified level, meaningthat it must trade through the barrier,either from above or below. Many othertrigger conditions are possible, however.Some examples include:■■ the spot must breach the trigger,

and remain above/below it for aspecified time;

■■ the spot trades at the trigger level at aspecified time (eg, expiry) or at anytime during the option’s life;

■■ the spot trades within or breaks out ofa range (for example, range binaries);

■■ there is more than one trigger level,with the payout conditional upon orincreasing with the number of triggersactivated and possibly the order inwhich they are activated (for example,a mini-premium option);

■■ some combination of these.See also barrier option, Parisian barrier option, range binary

Trigger forwardThe trigger forward is primarily designed for trading purposes,although it can also be used as analternative hedge. It is usually a zero-coststructure, whereby the purchaser entersinto an outright forward transaction at arate significantly more attractive than theprevailing market rate, but where thewhole structure will be knocked out if apredetermined trigger level is reached atany time before the expiry date.

Trinomial tree Similar to a binomial tree, a trinomialtree is a discrete-time model describingthe distribution of assets. After each time step in the trinomial tree there are three possible outcomes; an upmove, a down move or no move in theasset value. This gives additional degrees of freedom, which enhance the computational power of the lattice model.

TurboA type of path-dependent option,usually embedded in warrants. A barrier isset at the same level as the strike price,and if the underlying ever touches thebarrier at any point during the life of theturbo option, this will immediately causethe warrant to expire worthless. If theunderlying never reaches the strike


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T/U/Vduring the option’s life, the payout will besimilar to a vanilla warrant.

Two-factor model Any model or description of a system thatassumes two sources of uncertainty orvariables; for example, an asset price andits volatility (a stochastic volatility model),or interest rate levels and curve steepness(a stochastic interest rate model).Two-factor models model interest rate curvemovements more realistically than one-factor models.

Two-name exposureCredit exposure that the protection buyer has to the protection seller,which is contingent on the performance ofthe reference credit. If the protection sellerdefaults, the buyer must find alternativeprotection and will be exposed to changesin replacement cost due to changes incredit spreads since the inception of theoriginal swap. More seriously, if theprotection seller defaults and the referenceentity defaults, the buyer is unlikely torecover the full default payment due,although the final recovery rate on theposition will benefit from any positiverecovery rate on obligations of both thereference entity and the protection seller.

UUnderlyingThe underlying of a structured

product or option can be any asset class(equity index, stock basket, debtinstrument, interest rate, commodity or acombination of these) that is used toconstruct the product and whoseperformance is a key determinant of thepayout. In some products, the underlyingmay be a basket of 20 stocks, but theredemption basket that is used tocalculate the maturity payout maycomprise only 10 of those stocks.

UnderwaterHas the same meaning as out-of-the-money.

Up-and-inA type of barrier option that pays off only when the underlying index reaches the upper barrier during the lifeof the option.

Up-and-outA type of barrier option that knocks out when the underlying reachesthe strike.

VValue-at-riskFormally, the probabilistic bound ofmarket losses over a given period of time(known as the holding period) expressedin terms of a specified degree of certainty(the confidence interval). Put more simply,the value-at-risk (VaR) is the worst-case




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loss expected over the holding periodwithin the probability set out by theconfidence interval. Larger losses arepossible, but with a low probability. Forinstance, a portfolio whose VaR is $20million over a one-day holding period, witha 95% confidence interval, would haveonly a 5% chance of suffering an overnightloss greater than $20 million. Calculation ofVaR entails modelling the possible marketmoves over the holding period,incorporating correlations among marketfactors, calculating the impact of suchpotential market moves on portfoliopositions, and combining the results toexamine risk at different levels ofaggregation.The three main approachesto this analysis are historical simulation,the analytical approach using a correlationmatrix or empirical (Monte Carlo)simulation. Major trading houses expendconsiderable energies on their VaRmethodologies and have lobbiedregulators to recognise their efforts, withsome success.

Vanilla optionAlso known as a plain vanilla option. Avanilla option is a standard call or putoption in its most basic form.

VannaThe vega of an option is not constant.Vega changes as spot changes and asvolatility changes. The vanna of anoption measures the change in vega fora change in the underlying spot.As spot moves deeper out-of-the-money

for a vanilla option the vega is lower. Ifspot and volatility movements arepositively correlated the holder of anoption with positive vanna will beexpected to profit from this correlation.See also vega

Variable notional option/swapAn option or swap where the notionalvalue is linked to the underlying assetprice or rate. Usually changes in thenotional will be directly proportional tochanges in the underlying price; ie, theyboth decrease or increase together. Suchderivatives have two main uses. In anequity swap, the fixed-rate receiver canopt to receive the return of either a fixed number of stocks, or the number of stocks that could be purchased for a fixed sum.The former case amounts to a variable notional amountfor the swap. An example using an option is the case of a firm that sells more exports as exchange ratesdecline and its products thereforebecome cheaper abroad. Since it now has greater foreign currency revenueto hedge, it would purchase a variablenotional currency option for this purpose.

Variance gamma modelA jump model that better captures thecharacteristics of the volatility smile forshorter-dated options than stochasticvolatility models.

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Vequal to notional multiplied by thedifference between the realised varianceof the underlying index over the life ofthe swap and the strike variance.

Vasicek model An interest rate model that incorporatesmean reversion and a constant volatility for the short interest rate. It is a one-factor model from whichdiscount bond prices and options onthose bonds can be deduced. All haveclosed-form solutions.

Vega Measures the change in an option’s pricecaused by changes in volatility.Vega is atits highest when an option is at-the-money. It decreases the more the marketand strike prices diverge. Options closerto expiration have a lower vega thanthose with more time to run. Positionswith positive vega will generally havepositive gamma.To be long vega (to havea positive vega) is achieved by purchasingeither put or call options. Positions thatare long vega benefit from increases inimplied volatility but also from actualvolatility if the option is being deltahedged.They will also lose fromreductions in volatility. Spread optionscan be an exception: a reduction in thevolatility of one of the assets may actually increase the price of the optionbecause the correlation between the twoassets decreases.Vega is sometimesknown as kappa or tau. See also gamma,vanna, vomma

Vertical spread Any option strategy that relies on thedifference in premium between twooptions on the same underlying with thesame maturity, but different strike prices.Thus put spreads and call spreads wouldboth be vertical spreads.

Volatility A measure of the variability (but not thedirection) of the price of the underlyinginstrument. It is defined as the annualisedstandard deviation of the natural log ofthe ratio of two successive prices.Historical volatility is a measure of thestandard deviation of the underlyinginstrument over a past period. Impliedvolatility is the volatility implied in theprice of an option. All things being equal,higher volatility will lead to higher vanillaoption prices. In traditional Black-Scholesmodels, volatility is assumed to beconstant over the life of an option. Sincetraders mainly trade volatility, this isclearly unrealistic. New techniques havebeen developed to cope with volatility’svariability.The best known are stochasticvolatility, Arch and Garch.

Volatility skew The difference in implied volatilitybetween out-of-the-money puts andcalls. In most equity option markets out-of-the money calls have lowerimplied volatility than out-of-the-money puts.This is mostly ascribed to the greater supply of volatilityabove, rather than below, the money




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since fund managers are happy to writecalls and not so happy to write puts.Volatility skews can be very pronouncedin the currency markets althoughwhether puts or calls are favoureddepends on market sentiment anddemand and supply. See also impliedvolatility, risk reversal

Volatility smile A graph of the implied volatility of anoption versus its strike (for a given tenor) typically describes a smile-shaped curve – hence the term‘volatility smile’. This can be attributed tothe belief that the underlyingdistribution is leptokurtic, since thistends to increase the value of out-of-the-money options.

Volatility swapThe cash payout of a volatility swap is equal to notional multiplied by the difference between therealised volatility of the underlying index over the life of the swap and the strike volatility.

Volatility term structure The term structure of volatility is thecurve depicting the differing impliedvolatilities of options with differingmaturities. Such a curve arises partlybecause implied volatility in shortoptions changes much faster than forlonger options. However, the volatilityterm structure also arises because ofassumed mean reversion of volatility. The

effect of changes in volatility on theoption price is less the shorter theoption. Most market-makers takeadvantage of differing volatilities tohedge their books or to trade perceivedanomalies in volatility. Such strategieshave to be weighted because of thediffering vega effects. See also implied volatility

Volatility trading A strategy based on a view that futurevolatility in the underlying will be moreor less than the implied volatility in theoption price. Option market-makers arevolatility traders. The most common wayto buy/sell volatility is to buy/sell options,hedging the directional risk with theunderlying. Volatility buyers make moneyif the underlying is more volatile than theimplied volatility predicted. Sellers ofvolatility benefit if the opposite holds.Other methods of buying/sellingvolatility are to buy/sell combinations ofoptions, the most usual being to buy/sellstraddles or strangles. Other strategiestake advantage of the differencebetween implied volatilities of differingmaturity options, not between impliedand actual volatility. For example, ifimplied volatility in short-term options ishigh and in longer options low, a tradercan sell short-term options and buylonger ones.

Vomma The vega of an option is not constant.Vega changes as spot changes and as


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V/Wvolatility changes.The vomma of anoption is defined as the change in vegafor a change in volatility.Vommameasures the convexity of an option pricewith respect to volatility.Vega is tovomma (volatility gamma) as delta is togamma for spot movements. Holders ofoptions with a high vomma benefit fromvolatility of volatility. See also vega

WWarrant

An instrument giving the purchaser theright, but not the obligation, to purchaseor sell a specified amount of an asset at acertain price over a specified period oftime.Warrants differ from options only inthat they are usually listed. Underlyingassets include equity, debt, currencies andcommodities. See also equity warrant

Wasting assetA wasting asset is a derivative securitythat loses value due to time decay andwhich may expire worthless at maturity. Derivatives such as options,rights and warrants are considered to be wasting assets.

Weather derivativeTypically swaps and vanilla options suchas calls, puts, caps, floors and collars withpayouts linked to temperature,precipitation, humidity or windspeed.Most instruments are linked to heating

degree days or cooling degree days.These two indexes measure the deviationof the average of a day’s high and lowtemperature from a baseline referencetemperature.

Wedding cake depositA type of range deposit where there is aninner range and one or more outerranges.The payout from the product is atits maximum when the underlyingremains in the inner range, and this isreduced successively when the spotreaches each outer range.This product is suitable for investors who have a range-bound view, and want totake less risk.

Weekly reset forwardA weekly reset forward is a syntheticforward where a portion of the contract islocked in each week, provided that thespot rate that week meets apredetermined fixing criterion.Hence the purchaser can deal at a ratebetter than the forward outright, but only in an amount corresponding to the frequency with which the criterionhas been met. If the criterion is met innone of the weeks during the life of thecontract, then the contract is notactivated at all; if it is met every week,the overall rate is favourable compared with the initial prevailingmarket rate.The weekly reset forward is used for those with cash-flows spread over time or to hedge balance sheets.




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Window barrierA window barrier is a type of barrieroption for which the barrier strike onlyapplies for a specified period during theoption’s life. If the spot breaches this levelduring the window period, then theoption either knocks in or knocks out. Ifthe option is not activated during thewindow period, the option will retain thefeatures of a vanilla option and expire at maturity.

Worst-of optionAn option whose payout is referenced toone or more of the worst performers in abasket of shares or indexes.

YYield The interest rate that will make thepresent value of the cashflows from aninvestment equal to the price (or cost) ofthe investment. Also called the internalrate of return.The current yield relates theannual coupon yield to the market priceby dividing the coupon by the pricedivided by 100 and ignores the time valueof money or potential capital gains orlosses. Simple yield to maturity takes intoaccount the effect of the capital gain orloss on maturity of a bond in addition tothe current yield.

Yield adjustmentA payment by one counterparty, usually

at the outset of a swap or at a reset date,to compensate the other counterparty forentering into a swap on off-market terms.

Yield curveThe yield curve is a graphicalrepresentation of the term structure ofinterest rates. It is usually depicted as thespot yields on bonds with differentmaturities but the same risk factors(such as creditworthiness of issuer),plotted against maturity. The usualfeatures of a spot yield curve are higherlong-term yields than short-term yieldsand a curve for default-free bonds that islower at each point than the equivalentcurve for riskier debt. It is possible toconstruct variants of the yield curvefrom this basic form. The par yield curve is found by calculating thecoupons that would be necessary forbonds of each maturity to be priced atpar; the forward yield curve is found byextrapolating the spot yield curve point-by-point, based on the implied forwardinterest rates.

Yield curve agreement See yield curve swap

Yield curve option An option that allows investors to take aview on the shape of a yield curvewithout taking a view on a bond market’sdirection. It is normally structured as theyield of a longer maturity bond minus theyield of a shorter one. A call wouldtherefore appreciate in value as a curve


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Y/Zflattened. A put would decrease in value.Such options were developed in the US in1991 in response to a steepening yield curve.

Yield curve swap A swap in which the two interest streamsreflect different points on the swap yieldcurve.Yield curve swaps can be used toexploit a yield curve steepening orflattening view. For example, one sidepays the two-year Constant MaturityTreasury (CMT) rate and the other the 10-year CMT rate.

ZZero cost collarSee zero cost option

Zero cost option Any option strategy that involvesfinancing an option purchase by thesimultaneous sale of another option sothat paid and received premiums exactly

offset one another. See also collar,participating forward

Zero coupon bondA debt instrument issued at below par value.The bond pays no coupons;instead, it is redeemed at face value at maturity.

Zero coupon swap An off-market swap in which either orboth of the counterparties makes onepayment at maturity. Usually it is thefixed-rate payments only that aredeferred.The party not receivingpayment until maturity incurs a greater credit risk than it would with an ordinary swap.The swap isadvantageous for a company that will not receive payment for a projectuntil it is completed or to hedge zerocoupon liabilities, such as zero coupon bonds.

Zero exercise price option (ZEPO)A low exercise price option whose strikeprice is exactly zero.




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The ABC of Structured Products

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