THE OF EQUITY DERIV ATIVES AND STRU CTU RED P RODU CTS … Derivatives/SG Derivatives...

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AND STRUCTURED PRODUCTSOF EQUITY DERIVATIVES

2007

1 Equity Derivatives Glossary

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ACCRETING

A description, applicable to a variety of instruments, denoting that the notional principal increases successively over the life of the instrument, eg, caps, collars, swaps and swaptions. If the increase takes place in increments, the instrument may be known as a step-up. See also amortising

ACCRUAL CORRIDOR

The range within which an underlying reference rate must trade for coupon payments to accrue in a range note or corridor option.

ACCRUAL NOTE

See range note

ACCRUAL PERIOD

Period over which net payment or receipt pertaining to swaps is accrued. It is inclusive of the start date and runs to the end date without including the end date.

ALL-OR-NOTHING OPTION

See binary option

ALPHA

Alpha is used to measure the performance of a fund in relation to its benchmark. An alpha hat measures 2.0 indicates a fund has achieved a return 2% better than could have been expected from its benchmark. Alternative risk transfer An approach to risk management combining capital markets, reinsurance and investment banking techniques that allows a party to either free itself from risks not easily transferred via traditional insurance, or alternatively cover such risks in a non-traditional way – by using the capital markets for example.

ALTIPLANO

An Altiplano is a type of mountain range structure, which offers investors a fixed payout at the end of the product’s life on the condition that none of the assets that make up the underlying basket have decreased below a given level. If the level is breached, the product pays a capital guarantee plus participation in the growth of the total underlying basket.

AMERICAN-STYLE OPTION

The holder of an American-style option has the right to exercise the option at any time during he life of the option, up to and including the expiry date. See also option styles

AMORTISING

A description, applicable to a variety of instruments, denoting that the notional principal decreases successively over the life of an instrument, eg, amortising swap, index amortising rate swap, amortising cap, amortising collar, amortising swaption. If the decrease takes place in increments, the instrument may be known as a step-down. Mortgage-style amortisation refers to an amortising swap such that the principal amortisation plus interest is the same amount in each interest period. See also accreting

ANNAPURNA

An Annapurna is a kind of mountain range product, which offers a return equal to the greater of a capital guarantee plus a fixed coupon and a participation in the performance of the underlying basket. The level of the fixed coupon and of the participation rate in the performance depend on if and when the worst-performing stock breaches a downside barrier. The later the breach, the higher the fixed coupon and equity participation rate.

ANNUITY SWAP

An interest rate swap in which a series of irregular cashflows are exchanged for a stream of regular cashflows of equivalent present value.

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ARBITRAGE

A guaranteed or riskless profit from simultaneously buying and selling instruments that are perfect equivalents, the first being cheaper than the second.

ARBITRAGE-FREE MODEL

Any model that does not allow arbitrage on the underlying variable. Some simple early models assumed parallel shifts in the yield curve, but the varying yields of different duration bonds could be arbitraged using butterfly strategies.

AUTOREGRESSIVE CONDITIONAL

heteroscedasticity (Arch) A discrete time model for a random variable. It assumes that variance is stochastic and is a function of the variance of previous time steps and the level of the underlying.

ASIAN OPTION

See average option

ASSET ALLOCATION

The distribution of investment funds within a single asset class or across a number of asset classes (such as equities, bonds and commodities) with the aim of diversifying risk or adding value to a portfolio. See also overlay

ASSET BACKED SECURITY

An asset backed security is a security collateralised by assets such as bonds, credit card repayments, loan repayments or real estate.

ASSET SWAP

A package of a cash credit instrument and a corresponding swap that transforms the cash lows of the non-par instrument (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 a spread, although cross-currency asset swaps, transforming cashflows from one currency to another are also common.

ASSET/LIABILITY MANAGEMENT

The practice of matching the term structure and cashflows of an organisation’s asset and liability portfolios in order to maximise returns and minimise risk. An institutional example of this would be a bank converting a fixed-rate loan (asset) by utilising a fixed-for-floating interest rate swap to match its floating rate funding (deposits).

AT-THE-MONEY

1.At-the-money forward: An option whose strike is set at the same level as the prevailing market price of the underlying forward contract. With a Black-Scholes model, the delta of a European-style, at-the-money forward option will be close to 50%. 2.At-the-money spot: An option whose strike is set the same as the prevailing market price of the underlying. Because forwards commonly trade at a premium or discount to the spot, the delta may not be close to 50%. See also in-the-money, out-of-the-money

AUTOCAP

A standard cap consists of a series of caplets hedging future floating rate payments. However, autocaps only provide a hedge for the first pre-specified number of in-the-money caplets after which the option expires, and so are a cheaper alternative to caps.

AVERAGE OPTION

A plain vanilla option pays out the difference between its predetermined strike price and the spot rate (or price) of the underlying at the time of expiry. The purchaser of an average option (average price, average strike, average hybrid, average ratio), on the other hand, will receive a pay-out which depends on the average value of the underlying. The average can be calculated in a number of ways (arithmetic or geometric, weighted or simple) from the spot rate on a predetermined series of dates. An average rate (or average price) option is a cash-settled option with a predetermined (ie fixed) strike which is exercised at expiry against the average value of the underlying over the specified dates. In general, hedging with an average option is cheaper than using a portfolio of vanilla options, since the averaging process offsets high values with

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low ones and therefore lowers volatility and premium. Average options, also known as Asian options, are particularly popular in the equity, currency and commodity markets. In contrast, the strike for an average strike option is not fixed until the end of the averaging period which is typically much before the expiry. When the strike is set, the option is exercised against the prevailing spot rate. Unlike average price options, average strike options may be either cash or physically settled. In the case of an average hybrid option (also known as an average-in/average-out option), both the strike and settlement price of the option are determined using the average, where the strike averaging period typically precedes the settlement price averaging period. For the average ratio option, both the strike and settlement price of the option are determined using the average as in the hybrid case.The final payout is determined by comparing the ratio of settlement price to strike and a fixed percent strike.

AVERAGE PRICE OPTION

See average option

AVERAGE RATE OPTION

See average option

AVERAGE STRIKE OPTION

See average option

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BACK-TESTING

The validation of a model by feeding it historical data and comparing the model’s results with the historical reality. The reliability of this technique generally increases with the amount of historical data used.

BARRIER OPTION

Barrier options, also known as knock-out, knock-in or trigger options, are path-

dependent options which are either activated (knocked-in) or terminated (knocked-out) if a specified spot rate reaches a specified trigger level (or levels) between inception and expiry. Before termination knock-out options behave identically to standard European-style options, but carry lower initial premiums because they may be extinguished before reaching maturity. In contrast, knock-in options behave identically to European-style options only if they are activated/ knocked-in and so also command a lower premium. The standard barrier options have barrier levels that are monitored continually during the lifetime of the option. Single barrier options that have a barrier level above current spot are classified as up-and-out or up-and-in options. For single barriers below spot the usual terminology is down-and-out for the knock-out barrier option, and down-and-in for the knock-in barrier option. Many variations on the barrier theme are available. Barrier levels can be monitored continually, at discrete fixing times (discrete barrier options) or only at the final expiry date of the option (at-expiry barrier options). Barriers may be active only during distinct time intervals (window barrier options) or may change value at fixed points during the lifetime of the option (stepped barrier options). Barriers may need to be breached for a certain time before they are considered triggered (Parisian Barrier Options) or may allow for partial triggering depending upon how far beyond the trigger level the underlying asset is observed (Soft Barrier options). Barriers may reference a different underlying to that of the option itself – such barriers are known as outside barriers. See also discrete barrier option, double barrier option, Parisian barrier option, path-dependent option, trigger, trigger condition

BASIS

1.The difference between the price of a futures contract and its theoretical value. 2.The convention for calculating interest rates. A bond can be 30/360 or actual/365 in the US, or 360/360 in Europe. Money market instruments can be actual/360 in the US or actual/365 in the UK and Japan.

BASIS RISK

In a futures market, the basis risk is the risk that the value of a futures contract does not

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move in line with the underlying exposure. Because a futures contract is a forward agreement, many factors can affect the basis. These include shifts in the yield curve, which affect the cost of carry; a change in the cheapest-to-deliver bond; supply and demand; and changing expectations in the futures market about the market’s direction. Generally, basis risk is the risk of a hedge’s price not moving in line with the price of the hedged position. For example, hedging swap positions with bonds incurs basis risk because changes in the swap spread would result in the hedge being imperfectly correlated. Basis risk increases the more the instrument to be hedged and the underlying are imperfect substitutes.

BASIS SWAP

An interest rate basis swap or a cross-currency basis swap is one in which two streams of floating rate payments are exchanged. Examples of interest rate basis swaps include swapping $Libor payments for floating commercial paper, Prime, Treasury bills, or Constant Maturity Treasury rates; this is also known as a floating-floating swap. A typical cross-currency basis swap exchanges a set of Libor payments in one currency for a set of Libor payments in another currency.

BASIS TRADING

To basis trade is to deal simultaneously in a derivative contract, normally a future, and the underlying asset. The purpose of such a trade is either to cover derivatives sold, or to attempt an arbitrage strategy. This arbitrage can either take advantage of an existing mispricing (in cash-and-carry arbitrage) or be based on speculation that the basis will change. See also cash-and-carry arbitrage

BASKET CREDIT DEFAULT SWAP

A credit default swap which transfers credit risk with respect to multiple reference entities. For each reference entity, an applicable notional amount is specified, with the notional of the basket swap equal to the aggregate of the specified applicable notional amounts.

Types of basket credit default swaps include linear basket credit default swaps, first-to-default basket credit default swaps, and first-loss basket credit default swaps. See also credit default swap

BASKET OPTION

An option that enables a purchaser to buy or sell a basket of currencies, equities or bonds.

BASKET SWAP

A swap in which a floating leg is based on the returns on a basket of underlying assets, such as equities, commodities, bonds, or swaps. The other leg is usually (but not always) a reference interest rate such as Libor, plus or minus a spread.

BASKET TRADING

See program trading

BEAR SPREAD

An option spread trade that reflects a bearish view on the market. It is usually understood as the purchase of a put spread. See also bull spread, call spread

BERMUDAN OPTION

The holder of a Bermudan option, also known as a mid-Atlantic option, has the right to exercise it on one or more possible dates prior to its expiry. See also option styles

BEST-OF OPTION

A best-of option pays out on the best performing of a number of underlying assets over an agreed period of time. For instance, if a basket contains stock A, stock B and stock C and stock B gains in value by the larger amount during the products term, then the payout would be based on the increase in value of Stock B.

BETA

1. The beta of an instrument is its standardised covariance with its class of instruments as a whole. Thus the beta of a stock is the extent to which that stock follows movements in the overall market. 2. Beta trading is used by currency traders if they take the volatility risk of one currency in

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another. For example, rather than hedge a sterling/yen option with another sterling/yen option, a trader, either because of liquidity constraints or because of lower volatility, might hedge with euro/yen options. The beta risk indicates the likelihood of the two currencies’ volatilities diverging.

BETTER-OF-TWO-ASSETS OPTION

See best-of option

BILATERAL NETTING

Agreement between two counterparties whereby the value of all in-the-money contracts 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-product and encompass portfolios of swaps, interest rate options, and forward foreign exchange.

BINARY OPTION

Unlike simple options, which have continuous pay-out profiles, that of a binary option is discontinuous and pays out a fixed amount if the underlying satisfies a predetermined trigger condition but nothing otherwise. Binary options are also known as digital or all-or-nothing options. There are two major forms: at maturity and one-touch. At maturity binaries, also known as European binaries or at expiry binaries, pay out only if the spot trades above (or below) the trigger level at expiry. One-touch binary options, also known as American binaries, pay out if the spot rate trades through the trigger level at any time up to and including expiry. The pay-out of a one-touch binary may be due as soon as the trigger condition is satisfied or alternatively at expiry (one-touch immediate or one-touch deferred binaries). As with barrier options, variations on the theme include discrete binaries, stepped binaries, etc. Binary options are frequently combined with other instruments to create structured products, such as contingent premium options.

BINOMIAL MODEL

Any model that incorporates a binomial tree.

BINOMIAL TREE

Also called a binomial lattice. A discrete time model for describing the evolution of a random variable that is permitted to rise or fall with given probabilities. After the initial rise, two branches will each have two possible outcomes and so the process will continue. The process is usually specified so that an upward movement followed by a downward movement results in the same price, so that the branches recombine. If the branches do not recombine it is known as a bushy, or exploded, tree. The size of the movements and the probabilities are chosen so that the discrete binomial model tends to the normal distribution assumed in option models as the number of discrete steps is increased. Options can be evaluated by discounting the terminal pay-off back through the tree using the determined probabilities. Interest in binomial trees arises from their ability to deal with American-style features and to price interest rate options. For example, American-style options can readily be priced because the early exercise condition can be tested at each point in the tree.

BLACK-DERMAN-TOY MODEL

A one-factor log-normal interest rate model where the single source of uncertainty is the short-term rate. The inputs into the model are the observed term structure of spot interest rates and their volatility term structure. The Black-Derman-Toy model, such as the Ho-Lee model, describes the evolution of the entire term structure in a discrete-time binomial tree framework. The model can be used to price bonds and interest rate-sensitive securities, though the solutions are not closed-form.

BLACK-SCHOLES MODEL

The original closed-form solution to option pricing developed by Fischer Black and Myron Scholes in 1973. In its simplest form it offers a solution to pricing European-style options on assets with interim cash pay-outs over the life of the option. The model calculates the theoretical, or fair value for the option by constructing an instantaneously

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riskless hedge: that is, one whose performance is the mirror image of the option pay-out. The portfolio of option and hedge can then be assumed to earn the risk-free rate of return. Central to the model is the assumption that market returns are normally distributed (ie have lognormal prices), that there are no transaction costs, that volatility and interest rates remain constant throughout the life of the option, and that the market follows a diffusion process. The model has five major inputs: the risk-free interest rate, the option’s strike price, the price of the underlying, the option’s maturity, and the volatility assumed. Since the first four are usually determined by the market, options traders tend to trade the implied volatility of the option.

BOND

Companies or governments issue bonds as a means of raising capital. The bond purchaser is in effect making a loan to the issuer, and unlike with shares investors at no point hold a stake in the company.

BOND INDEX SWAP

A swap in which one counterparty receives the total rate of return of a bond market or segment of a bond market in exchange for paying a money market rate. Counterparties may also swap the returns 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 certain strike put is underpriced, the trader buys the put and sells a call at the same strike, creating a synthetic short futures position. To get rid of the market risk, he sells another put and buys another call, but at different strike prices. See also convergence trade

BRACE-GATAREK-MUSIELA (BGM) MODEL

See market model of interest rates.

BULL SPREAD

An option spread trade that reflects a bullish view on the market. It is usually

understood as the purchase of a call spread. See also bear spread, call spread

BUTTERFLY SPREAD

The simultaneous sale of a straddle and purchase of a money strangle. The structure profits if the underlying remains stable, and has limited risk in the event of a large move in either direction. As a trading strategy to capitalise upon a range trading environment it is usually executed in equal notional amounts. Alternatively, such trades are often applied to benefit from changes in volatility. In such circumstances the butterfly spread is traded on a ‘vega-neutral’ basis (ie the volatility sensitivity of the long position is initially offset by the volatility sensitivity of the short position). As the holder of an initially vega-neutral spread, the trader will benefit from changes in volatility since the strangle position profits more from an increase in volatility than the straddle and loses less than the straddle in a decline in volatility (this is due to the fact that the vomma of the strangle is higher than that of the straddle).

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CALENDAR SPREAD

A strategy that involves buying and selling options or futures with the same (strike) price but different maturities. Such a strategy is used in futures when one contract month is theoretically cheap and another is expensive. With options, the strategy is often used to play the shape of or expected changes in, the volatility term structure. For example, if one-month volatility is high and one-year volatility low, arbitrageurs might buy one-year straddles and sell short-term straddles, thereby selling short-term volatility and buying long-term volatility. If, all else being equal, short-term volatility declines relative to long-term volatility, the strategy makes money.

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CALL OPTION

See option

CALL SPREAD

A strategy that reduces the cost of buying a call option by selling another call at a higher strike price (Bull call spread). This limits potential gain if the underlying goes 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 only limited upside in the underlying. Alternatively a Bear call spread can be constructed by selling a call option and buying another at a higher strike price. See also bear spread, bull spread, put spread

CALLABLE SWAP

An interest rate swap in which the fixed-rate payer has the right to terminate the swap after a certain time if rates fall. Often done in conjunction with callable debt issues where an issuer is more concerned with the cost of debt than the maturity. The embedded option is, in effect, a swaption sold by the fixed-rate receiver which enables the fixed-rate payer to receive the same high fixed rate for the remaining years of the swap in the event that interest rates fall. The fixed rate received under the swaption offsets the fixed rate paid under the original swap effectively cancelling the swap. In some definitions of a callable swap, the fixed-rate receiver has the right to terminate the swap. Also known as a cancellable swap.

CANCELLABLE SWAP

See callable swap

CAP

A contract whereby the seller agrees to pay to the purchaser, in return for an upfront premium or a series of annuity payments, the difference between a reference rate and an agreed strike rate when the reference exceeds the strike. Commonly, the reference rate is three- or six-month Libor. A cap is therefore a strip of interest rate guarantees that allows the purchaser to take advantage of a reduction in interest rates and to be

protected if they rise. They are priced as the sum of the cost of the individual options, known as caplets. See also collar

CAPITAL-PROTECTED

A structured product that provides capital protection offers an amount that at least matches a given proportion of the investor’s original capital input at maturity. Can also be referred to as principal-protected. Capital-protected credit-linked note A credit-linked note where the principal is partly or fully guaranteed to be repaid at maturity. In a 100% principal-guaranteed credit-linked note, only the coupons paid under the note bear credit risk. Such a structure can be analysed as (i) a Treasury strip and (ii) a stream of risky annuities representing the coupon, purchased from the note proceeds minus the cost of the Treasury strip. See also credit-linked note

CAPPED FLOATER

A floating-rate note which pays a coupon only up to a specified maximum level of the reference rate. This is done by embedding a cap in a vanilla note where the investor effectively sells the issuer a cap. A capped floater protects the debt issuer from large increases in the interest rate environment.

CAPPED SWAP

An interest rate swap with an embedded cap in which the floating payments of the swap are capped at a certain level. A floating-rate payer can thereby limit its exposure to rising interest rates.

CAPTION

An option on a cap. A type of compound option in which the purchaser has the right, but not the obligation, to buy or sell a cap at a predetermined price on a predetermined date. Captions can be a cheap way of leveraging into the more expensive option. See also floortion

CASH AND CARRY

When a contango exists, the premium of the forward position over the spot generally reflects costs of buying and holding (eg financing, transaction costs, insurance,

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custody) for that period. See also cash and carry arbitrage

CASH MARKET

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

CASH-AND-CARRY ARBITRAGE

A strategy, used in bond or stock index futures, in which a trader sells a futures contract and buys the underlying to deliver into it, to generate a riskless profit. For the strategy to work, the futures contract must be theoretically expensive relative to cash. Cash-and-carry arbitrage and reverse cash-and-carry arbitrage typically keep the futures and underlying markets closely aligned. See also basis trading, reverse cash-and-carry arbitrage

CATASTROPHE BOND

A bond that pays a coupon that decreases only after a catastrophe such as a hurricane or earthquake with a specified magnitude in a specified region and period of time.

CATASTROPHE OPTION

These options can be American-style or European-style, either paying out if a single specified catastrophe such as a hurricane or earthquake occurs, or alternatively, having a pay-out dependent on an index. For example, the index may represent the number of claims received by property insurance companies.

CATASTROPHE RISK SWAP

An agreement between two parties to exchange catastrophe risk exposures. For example, in July 2001 Swiss Re and Tokyo Marine arranged a $450 million deal including three risk swaps: Japan earthquake for California earthquake, Japan typhoon for France storm and Japan typhoon for Florida hurricane. Swaps increase diversification and allow each of the parties to lower the amount of capital that they need to hold.

CHOOSER OPTION

A chooser option offers purchasers the choice, 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 want the put or the call.

CLIQUET

Cliquet structures, which can also be called ratchet structures, periodically settle and reset their strike prices, allowing users to lock-in potential profits on the underlying. With a cliquet the payout is worked out from the performance of the underlying asset in a number of set periods during the product’s life. See also ladder options

CLIQUET OPTION

Also known as a ratchet or reset option. A path-dependent option that allows buyers to lock-in gains on the underlying security during chosen intervals over the life time of the option.The option’s strike price is effectively reset on predetermined dates. Gains, if any, are locked in. So if an underlying rises from 100 to 110 in year one, the buyer locks in 10 points and the strike price is reset at 110. If it falls to 97 in the next year the strike price is reset at that lower level, no further profits are locked in, but the accrued profit is kept. See also ladder option, lookback option, moving strike option, path dependent option

CLOSED-FORM SOLUTION

Also called an analytical solution. An explicit solution of, for example, an option pricing problem by the use of formulae involving only simple mathematical functions, such as Black-Scholes or Vasicek models. Closed-form models can usually be evaluated much more quickly than numerical models, which are sometimes far 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 of interest rate options).The premium from selling the call reduces the cost of purchasing

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the put. The amount saved depends on the strike rate of the two options. If the premium raised by the sale of the call exactly matches the cost of the put, the strategy is known as a zero cost collar. The combination of purchasing the put and selling the call while holding the underlying protects the holder from losses if the underlying falls in price, at the expense 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 an interest rate swap. The transaction is zero cost – the purchase of the cap is financed by the sale of the floor. The collar constrains both the upside and the downside of a swap.

COLLARED FLOATER

A floating-rate note whose coupon payments are subject to an embedded collar. Thus the coupon is capped at a predetermined level, so the buyer forsakes some upside, but also floored, offering protection from a downturn in the reference interest rate. Also known as a mini-max floater.

COLLATERALISED BOND OBLIGATION (CBO)

A multi-tranche debt structure, similar to a collateralised mortgage obligation. But rather than mortgages, low-rated bonds serve as the collateral. See also collateralised mortgage obligation

COLLATERALISED DEBT OBLIGATION (CDO)

Generic name for collateralised bond obligations, collateralised loan obligations, and collateralised mortgage obligations. See also collateralised mortgage obligation, synthetic collateralised debt obligation

COLLATERALISED LOAN OBLIGATION (CLO)

A structured bond backed by the loan repayments from a portfolio of pooled personal or commercial loans, excluding mortgages. The structure allows a bank to remove loans from its balance sheet and

so reduce its required capital reserves, while retaining contact with the borrowers and fees from servicing the loans. See also collateralised mortgage obligation

COLLATERALISED MORTGAGE OBLIGATION

A type of asset-backed security, in this case backed by mortgage payments. Typically, such securities provide a higher return than normal fixed-rate securities but purchasers suffer prepayment risk if mortgage holders redeem their mortgages. Because the right to redeem the mortgage is effectively an embedded call, such securities have negative convexity. See also collateralised bond obligation, collateralised debt obligation, collateralised loan obligation

COMBO

See risk reversal

COMPOUND OPTION

A compound option is an option on an option. The tool allows the user to buy or sell an option at a fixed price during a set period. They are often used to hedge against increase in option prices during volatile periods. Examples include captions and floortions.

CONDOR

The simultaneous purchase (sale) of an out-of-the-money strangle and sale (purchase) of an even further out-of-the-money strangle. The strategy limits the profit or loss of the pay-out and is directionally neutral.

CONSTANT MATURITY SWAP

This is an interest rate swap where the floating interest arm is reset periodically with reference to longer duration treasury-based instruments rather than a market index such as LIBOR.

CONSTANT MATURITY TREASURY DERIVATIVE

Over-the-counter swaps and options which use longer-term, Treasury-based instruments for their floating rate reference than money market indexes, such as Libor.‘Constant Maturity Treasury’ (CMT) refers to the par yield that would be paid by a treasury bill, note or bond which matures in exactly one, two, three, five, seven, 10, 20 or 30 years.

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Since there may not be treasury issues in the market with exactly these maturities, the yield is interpolated from the yields on treasuries that are available. In the US, such rates have been calculated and published by the Federal Reserve Bank of New York and the US Treasury department on a daily basis every day for more than 30 years. The H.15 Report from the Federal Reserve Bank is often used as a source for CMT rates. It is then possible for this interpolated yield to form the index rate for instruments such as floating rate notes, which pay interest linked to the CMT yield, options, which pay the difference between a strike price and the CMT yield, and swaps and swaptions, in which one of the cashflows exchanged is the CMT yield. Where necessary, the reference rate is reset at each settlement date. Typical uses of CMT derivatives as hedging tools include the purchase of CMT floors by mortgage servicing companies to protect the value of purchased mortgage servicing portfolios, and the purchase of CMT caps to protect investors with negatively convex mortgage-backed securities portfolios. It is possible to enter into derivatives in other currencies that are based, by analogy, on a ‘constant maturity interest rate swap’ interpolated from the swap curve in the relevant currency. Such derivatives are known as constant maturity swap (CMS) derivatives. Unlike CMT derivatives, CMS derivatives incorporate the spread component of swaps.

CONSTANT PROPORTION PORTFOLIO

INSURANCE (CPPI)

A fund management technique that aims to provide maximum exposure to risky assets while still protecting investors’ capital. The technique requires the manager to dynamically rebalance the portfolio between risky assets (such as equities) and safe assets (such as bonds) according to a quantitative model. The level of risky assets is managed such that at all times, in the event of a market crash, the remaining NAV of the fund is still sufficient to meet the stated protection level. Generally the proportion of Risky Assets in the fund is increased when these

perform well and decreased when these perform poorly. The capital protection level may be fixed, or rachet up (reset) according to a certain percentage of the fund NAV achieved during the fund term.

CONTINGENT SWAP

The generic term for a swap activated when rates reach a certain level or a specific event occurs. Swaptions are often considered to be contingent swaps. Other types of swaps, for example, drop-lock swaps, are activated only 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 an agreement made between two parties to exchange (at the closing of the contract) a cashflow equivalent to the difference between the opening and closing prices, multiplied by the number of shares detailed in the contract. CFDs are traded on margin, do not incur stamp duty and can have individual stocks or indexes as the underlying.

CONVERGENCE TRADE

Trading strategy where similar securities are bought and sold simultaneously in the expectation that prices will converge in an orderly fashion. 1.A way of taking advantage of mispriced options by creating a synthetic short futures position and hedging market risk by buying a futures contract against it. Thus if a put is undervalued, a trader buys it, at the same time selling a fairly valued call and buying a futures contract. The same strategy can be applied if the call is mispriced. If the option is truly undervalued, the trader earns a riskless profit. The whole exercise relies on put-call parity 2.The act of converting a convertible bond into equity. See also box, reversal

CONVERTIBLE BOND

A bond issued by a company that may be exchanged by the holder for a number of that company’s shares at a predetermined ratio, or at a discount to the share price at maturity. Because the convertible embeds a call option on the company’s equity, convertibles carry


much lower rates of interest than traditional debt and are therefore a cheap way for companies to raise debt. The problem for existing shareholders is that conversion dilutes the company’s outstanding shares. Typically, bonds are convertible into a company’s own stock. There are however ‘third party convertibles’, which convert into shares of another company. See also equity warrant, resettable convertible bond

CONVEXITY

A bond’s convexity is the amount that its price sensitivity differs from that implied by the bond’s duration. Fixed-rate bonds and swaps have positive convexity: when rates rise the rate of change in their price is slower than suggested by their duration; when rates fall it is faster. Positive convexity is therefore a welcome attribute. The higher the bond’s duration, the more its convexity. Bonds or swaps with call options or embedded call options, eg collateralised mortgage obligations, have negative convexity: when rates rise their price fall is faster relative to the interest rate move. Convexity effectively describes the same attribute as gamma.

CORRELATION

Correlation is a measure of the degree to which changes in two variables are related. It is normally expressed as a coefficient between plus one, which means variables are perfectly correlated (in that they move in the same direction to the same degree) and minus one, which means they are perfectly negatively correlated (in that they move in opposite directions to the same degree). In financial markets correlation is important in three areas: 1.The model used for global asset allocation decisions, Sharpe’s capital asset pricing model (CAPM), has, as its linchpin, a covariance matrix that measures correlations between markets. 2.Correlation is also central to the pricing of some options, where two-factor or multi-factor models are used. For spread options, yield curve options and cross-currency caps, estimating the correlation between the underlying assets is of primary importance, the degree of

correlation between them having a direct influence on the option price. For quantos such as guaranteed exchange rate options, or differential swaps, the correlation effect is the extent to which there is a relationship between movements in the underlying and movements in the ex-change rate, which has a secondary effect on the price of the option. 3.Correlation between markets is also used to offset an option position in one market against another with similar direction and volatility. Such a strategy might be used to reduce cost – to avoid hedging the positions separately, or because implied volatility in the second market is lower – or because hedging is difficult in the first market. Correlation can be estimated historically (like volatility) but tends to be unstable, and historic estimations may be poor predictors of future realised correlations. See also joint option

CORRELATION SWAP

An instrument that allows an investor to take financial exposure on a set of correlations.

CORRIDOR FLOATER

See range note

CORRIDOR OPTION

The holder of a corridor option receives a coupon at the end of the lifetime of the corridor whose magnitude depends upon the behaviour of a specified spot rate during the lifetime of the corridor. For each day on which the spot rate (typically an official fixing rate observation) remains within the chosen spot range (the accrual corridor) the holder accrues one day’s worth of coupon interest. A variation is the knockout corridor option. In this structure, the holder ceases to accrue coupon interest as soon as the spot rate leaves the range. Even if the spot rate subsequently re-enters the range, the holder does not continue to accrue coupon interest. At the end of the option’s lifetime, the accrued coupon is calculated according to the following formula: If the accrual corridor is one-sided (the other side of the range bing open-ended), it is known as a wall option. Typically, corridor options are imbedded in a structured note, sometimes called a range note, that pays a higher yield than the corresponding vanilla debt as long as the underlying rate remains

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sufficiently long within the accrual corridor. A similar option to the corridor option is the range binary, a binary option which pays a fixed coupon amount if the range is not breached but nothing if it is breached.

COST OF CARRY

The cost of financing an asset. If the cost is lower than the interest received, the asset has a positive cost of carry; if higher, the cost of carry is negative. The cost of carry is determined by the opportunities for lending the asset and the shape of the yield curve. So a bond, for example, would have a positive cost of carry if short-term rates (financing rates) were lower than the assets’s yield or (and) if the cost could be mitigated by lending out the securities. See also future

COUNTERPARTY CREDIT RISK

See credit risk

COVERED CALL

To sell a call option while owning the underlying security on which the option is written. The technique is used by fund managers to increase income by receiving option premium. It would be used for securities they are willing to sell, only if the underlying went up sufficiently for the option to be exercised. Generally, covered call writers would undertake the strategy only if they thought volatility was overpriced in the market. The lower the volatility, the less the covered call writer gains in return for giving up upside in the underlying. It provides downside protection only to the extent that the option premium offsets a market downturn. See also covered put

COVERED PUT

To sell a put option while holding cash. This technique is used to increase income by receiving option premium. If the market goes down and the option is exercised, the cash can be used to buy the underlying to cover. Covered put writing is often used as a way of target buying: if an investor has a target price at which he wants to buy, he can set the strike price of the option at that level and receive option premium to

increase the yield of the asset. Investors also sell covered puts if markets have fallen rapidly but seem to have bottomed, because of the high volatility typically received on the option. See also covered call

COVERED WARRANT

See warrant

COX-INGERSOLL-ROSS MODEL

In its simplest form this is a lognormal one-factor model of the term structure of interest rates, which has the short rate of interest as its single source of uncertainty. The model allows for interest rate mean reversion and is also known as the square root model because of the assumptions made about the volatility of the short-term rate. The model provides closed-form solutions for prices of zero-coupon bonds, and put and call options on those bonds.

CREDIT DEFAULT SWAP

A bilateral financial contract in which one counterparty (the protection buyer or buyer) pays a periodic fee, typically expressed in basis points per annum on the notional amount, in return for a contingent payment by the other counterparty (the protection seller or seller) upon the occurrence of a credit event with respect to a specified reference entity. The contingent payment is designed to mirror the loss incurred by creditors of the reference entity in the event of its default. The settlement mechanism may be cash or physical. See also basket credit default swap

CREDIT DERIVATIVE

A bilateral financial contract, which isolates credit risk from an underlying instrument and transfers that credit risk from one party to the contract (the protection buyer) to the other (the protection seller). There are two main categories of credit derivatives: the first consists of instruments such as credit default swaps in which contingent payments occur as a result of a credit event; the second, which includes credit spread options, seeks to isolate the credit spread component of an instrument’s market yield.

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CREDIT EVENT

Any one of a specified set of events, which, if occurring with respect to an obligation of the reference entity specified in a credit default swap, will trigger contingent payments. Applicable events, which generally include bankruptcy, repudiation/moratorium, restructuring, failure to pay, and cross-acceleration are determined by negotiation between the parties at the outset of a credit default swap.

CREDIT OPTION

Put or call options on the price of either (a) a floating rate note, bond, or loan, or (b) an asset swap package, consisting of a credit-risky instrument with any payment characteristics and a corresponding derivative contract that exchanges the cashflows of that instrument for a floating rate cashflow stream, typically three- or six-month Libor plus a spread.

CREDIT RISK

Also known as default risk. In broad terms, the risk that a loss will be incurred if a counterparty to a (derivatives) transaction does not fulfil its financial obligations in a timely manner. The term is sometimes loosely used as shorthand for the likelihood or probability of default, irrespective of the value of any position exposed to this risk. More precisely, credit risk is the risk of financial loss arising out of holding a particular contract or portfolio.

CREDIT SPREAD

A credit spread is the difference in yield between two debt issues of similar maturity and duration. The credit spread is often quoted as a spread to a benchmark floating-rate index such as Libor, or alternatively as a spread to a highly rated reference security such as a government security. The credit spread is often used as a measure of relative creditworthiness, with reduction in the credit spread reflecting an improvement in the borrower’s perceived creditworthiness.

CREDIT SPREAD FORWARD

A cash-settled forward contract with settlement amounts based on the credit

spread between two predetermined debt issues on the maturity date. See also credit spread option

CREDIT SPREAD OPTION

An option on the credit spread between two debt issues. The option will pay out the difference between the credit spread at maturity and a strike spread determined at the outset. See also credit spread forward

CREDIT-LINKED NOTE

A security with redemption and/or coupon payments linked to the occurrence of a credit event with respect to a specified reference entity. In effect, a credit-linked note embeds a credit default swap into a funded asset to create a synthetic investment that replicates the credit risk associated with a bond or loan of the reference entity. Credit-linked notes are typically issued on an unsecured basis directly by a corporation or financial institution. Credit-linked notes may also be issued from a collateralised Special Purpose Vehicle (SPV). See also capital-protected credit-linked note

CROSS-CURRENCY CAP

A cap in which the vendor will pay the purchaser the spread between interest rates (usually Libor-based) in different currencies minus a strike spread, where this exceeds zero, in return for a premium. It has the same relationship to a differential swap as a cap has to an interest rate swap. See also cross-currency floor

CROSS-CURRENCY FLOOR

This is an option setting a cap on the spread between two index interest rates in different currencies. See also cross-currency cap

CROSS-CURRENCY SWAP

A cross-currency swap involves the exchange of cashflows in one currency for those in another. Unlike single-currency swaps, cross-currency swaps often require an exchange of principal. Typically the notional principal is exchanged at inception at the prevailing spot rate. Interest rate payments are then passed back on a fixed,

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floating or zero basis. The principal is then re-exchanged at maturity at the initial spot rate.

CUMULATIVE CAP

A cumulative interest rate cap protects against increases in total interest expense over a specified period of time. This period of time will incorporate several rate settings in determining the final interest expense (for example, four three-month Libor settings for an annual interest expense amount). This differs from a standard cap, which caps an absolute rate of interest in each calculation period. Because a cumulative cap does not provide the period-to-period protection of a standard cap, it is generally cheaper than the corresponding standard cap.

CURRENCY FORWARD

An agreement to exchange a specified amount of one currency for another at a future date at a certain rate. The exchange of currencies is priced so as to allow no risk-free arbitrage. In other words, pricing is not a market estimate of the spot rate at that date, but is made according to the two currencies’ respective interest rates. For example, assuming that Eurosterling interest rates are 10% and Eurodollar 5%, and the US dollar/sterling spot rate is 1.75, the forward rate should reflect the 5% interest rate advantage of depositing money in sterling. Thus the 12-month forward rate should be 1.6695. Forwards are more appropriate than options if a company has a strong directional view of expected movements in exchange rates. But certainty is rare and hedging entirely with forwards may leave a company locked into unfavourable exchange rates. Unlike options, forwards do not enable companies to take advantage of favourable currency movements. The purchaser of a forward, unlike the purchaser of a future, carries the credit risk of the firm from which it makes the purchase. Since the contracts are not easily reassignable, it is difficult to reduce this risk.

CURRENCY OVERLAY

See overlay

CURRENCY PROTECTED OPTION

The same as guaranteed exchange rate or quanto option.

CURRENCY RISK

Currency risk arises from changes in the value of currencies. For example, if a company receives a portion of its income in a foreign currency, it is exposed to changes in the value of that currency. Risk management and derivatives can be used to minimise this risk.

CURRENCY STRUCK OPTION

This is the same as joint option.

CURRENT EXPOSURE

Another name for replacement cost.

CYLINDER

See risk reversal

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DEFERRED PAYOUT OPTION

A deferred payout option is a variation on American-style options similar to a shout option. The holder of the option may exercise it at any time, for the value taken by the underlying at that time, but the payout is delayed until the expiry date. This term is also applied to certain digital options whose payout is not paid when triggered, but deferred until the final maturity. See also option styles

DEFERRED START OPTION

See forward start option

DELAYED RESET SWAP

Also known as an in-arrears swap. A swap in which floating payment is based on the future, rather than present, value of the reference rate. For six-month delayed Libor reset swaps, for example, instead of fixing

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Libor six months and two days before the payment date, the floating-rate borrower delays fixing until two days before payment. Such swaps are popular in a steep yield curve environment, when a fixed-rate receiver may think rates will not rise as fast as the yield curve predicts.

DELTA

The delta of an option describes its premium’s sensitivity to changes in the price of the underlying. In other words, an option’s delta will be the amount of the underlying necessary to hedge changes in the option price for small movements in the underlying. The delta of an option changes with changes in the price of the underlying. An at-the-money option will have a delta of close to 50%. It falls for out-of-the-money options and increases for in-the-money options, but the change is non-linear: it changes much faster when 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 underlying in proportion to its delta. For example, if one is short a call option on an underlying with a face value of $1 million and a delta of 25%, a long position of $250,000 in the underlying will leave one delta-neutral with no exposure to small changes in the price of the underlying. Such a hedge is only effective instantaneously, however. Since the delta of an option is itself altered by changes in the price of the underlying, interest rates, the option’s volatility and its time to expiry, changes in any of these factors will shift the net position away from delta-neutrality. In practice, therefore, a delta-hedge must be rebalanced continuously if it is to be effective. See also static replication

DERIVATIVE

A derivative instrument or product is one whose value changes with changes in one 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 and

convertible bonds. In mathematical models of financial markets, derivatives are known as contingent claims.

DIFFERENCE OPTION

See spread option

DIFFUSION PROCESS

A continuous-time model of the behaviour of a random variable. An example of such a model is Generalised Brownian Motion (GBM), which is often used to model the behaviour of spot rates.

DIGITAL OPTION

Digital options pay a set amount if the underlying asset is above, or sometimes below, a certain level on a specific date. These options have only two possible outcomes: a set payout, or nothing at all. Thus, they are also known as binary or all-or-nothing options.

DIGITAL SWAP

A swap in which the fixed leg is only paid on each swap settlement date if the underlying has met certain trigger conditions over the period since the previous payment date. Nothing is paid if this is not the case. The premium for such a swap is amortised over the maturity of the swap and an instalment paid at each payment date.

DISCRETE BARRIER OPTION

Barrier options where the trigger level is only active for part of the option’s lifetime. This includes barrier options where the trigger is only valid on certain fixing dates, as well as cases where the trigger is valid for sub-intervals of the option’s lifetime. See also barrier option

DISTRIBUTION

The probability distribution of a variable describes the probability of the variable attaining a certain value. Assumptions about the distribution of the underlying are crucial to option models because the distribution determines how likely it is that the option will be exercised. Many models assume the logarithm of the relative return has a normal distribution, which can be described by two

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parameters. The first is the distribution’s mean; the second its standard deviation (equivalent, if annualised, to volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the skew (how much it tilts to one side or the other) and kurtosis, which describes how fat or thin are the tails at either side. Most markets tend to have fat tails (to be leptokurtic) rather than thin tails (platykurtic). This pushes up the price of out-of-the-money options.

DOUBLE BARRIER OPTION

This is an option with two barriers; one setting the upper limit of the price of the underlying and one setting the lower limit. If the underlying crosses either of these barriers the option is either activated (knock-in) or deactivated (knock-out). See also barrier option.

DOUBLE NO-TOUCH

A double no-touch option pays a set amount as long as one of two specified barrier levels are not broken during the life of the option. This tool is popular for usage in relatively stable markets.

DOWNSIDE RISK

The risk the investor is exposed to if there is a fall in the value of the underlying.

DUAL CURRENCY SWAP

Dual currency swaps are currency swaps that incorporate the foreign exchange options necessary to hedge the interest payments back into the principal currency for dual currency bonds.

DYNAMIC HEDGING

See delta hedging

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EMBEDDED OPTION

An option, often an interest rate option, embedded in a debt instrument that affects its redemption. Examples include mortgage-backed securities and callable and puttable bonds.

EMBEDDED OPTIONS

do not have to be interest rate options; some are linked to the price of an equity index (Nikkei 225 puts embedded in Nikkei-linked bonds) or a commodity (usually gold). Many so-called guaranteed products contain zero-coupon bonds and call options.

EQUILIBRIUM MODEL

A model that specifies processes for the underlying economic variables and the extra risk premium investors require for risky assets. The evolution of asset prices and their risk derived from the model thus specified.

EQUITY (INDEX) SWAP

A swap in which the total or price return on an equity index, equity basket or single equity is exchanged for a stream of cashflows based on a short-term interest rate index (or another index). Equity swaps are a convenient structure for switching into or out of equity markets, particularly for those that prefer to avoid, or are not allowed to use, stock index futures. Like futures, the price of the swap is directly related to the cost of carry, although there may also be tax considerations.

EQUITY COLLAR

Equity collars are used by investors keen to reduce their downside risk. An equity collar is formed by buying an equity put option with a strike price below the current value of the equity, at the same time as selling an equity call option with a strike above the current equity price. Thus a collar is imposed around the investor’s equity position. If the value of the underlying equity falls through the strike of the bought put, it can be exercised to limit losses. However, if the underlying stock rises

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through the strike of the sold call, the investor may have to deliver the equity at the strike, thus foregoing potential additional upside. See also collar

EQUITY KNOCK-OUT SWAP

An interest rate or cross-currency swap that gets terminated (knocked-out) if a given stock or equity-index reaches a specified trigger level between inception and expiry. The knock-out can be unconditional once the pre-determined equity level is reached, or the client can be given the choice to cancel the swap should the trigger level be reached.

EQUITY LINKED NOTE

An equity linked note is a tool that is linked to a single equity, equity index or basket of equities. They may or may not be principal protected.

EQUITY WARRANT

A warrant is a financial instrument issued by a bank or other financial institutions, which is traded on a stock exchange’s equity market. Warrants may be issued over securities such as shares in a company, a currency, an index or a commodity. A call warrant gives the holder the right (but not the obligation) to buy a given security at a given price known as the exercise price, on a given date, known as the expiry date. Conversely a put warrant gives the holder the right to sell the security at the exercise price on the expiry date. These instruments are sometimes known as covered warrants or derivative warrants. See also convertible bond, warrant

EUROPEAN-STYLE OPTION

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

EVEREST STRUCTURE

A capital guaranteed structure generally offering the investor the sum invested at maturity and potential upside linked to the

performance of the least-performing asset in a predefined basket. The Everest structure may also pay coupons over its life.

EXCHANGEABLE BOND

These are just like convertible bonds. The main difference is that these are typically issued on stock, which is not the stock of the issuing firm.

EXCHANGE-TRADED OPTION

See option

EXERCISE

See option

EXOTIC OPTION

Any option with a more complicated payout structure than a plain vanilla put or call option. The payout of a plain vanilla option is simply the difference between the strike price of the option and the spot price of the underlying at the time of exercise. For a European-style option, the exercise time is always the expiry date; other option styles offer greater flexibility. There are a number of ways in which an option payout can differ from that of a plain vanilla. The payout could also be a function of: ¦¦the difference between a strike and an average rate for the underlying (average options) ¦¦the difference between prices for two different underlyings (difference options, exchange options), the same underlying at different times (high-low options) ¦¦the correlation between two or more underlyings (outperformance options, outside barrier options) ¦¦the difference between a strike and the spot rate at some time other than expiry (deferred payout options, shout options, lookback options, cliquet options, ladder options) ¦¦a fixed amount (binary options) Alternatively, or additionally, a payout may be conditional on certain trigger conditions being met. For example, barrier options are activated or nullified if a spot rate falls or rises through a predetermined trigger level. Multiple trigger conditions are possible (as in the case of corridor or mini-premium options).

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EXPLODED TREE

A tree (binomial or trinomial) in which an up step followed by a down step gives a different outcome to a down step followed by an up step. Consequently, the number of nodes increases exponentially, compared with a recombining tree, in which the number increases quadratically. This makes their evaluation exceptionally computer-intensive. The advantage is that they can be used to price path-dependent options and they are important for modelling interest rate options.

EXTREME VALUE THEORY

An area of statistical research that focuses on modelling the extreme values of return distributions. This is important in finance because many models (for example the Black-Scholes Model) assume that the distribution of returns is log-normal. However, real-world distributions are found to have fat-tails – implying that rare events such as crashes are more likely than the traditional theories suggest.

F

FAT TAILS

See kurtosis

FINANCIAL ENGINEERING

The design and construction of investment products to achieve specified goals.

FLEXIBLE OPTION

A flexible option (also known as a flexible exchange or flex option) is a customisable exchange-traded option, which allows the buyer to customise contract terms such as expiry date and contract size in addition to the strike price. Flexible options with single stock, index, or even currency underlyings are traded on several major exchanges.

FLOOR FUND

Also known as a ratchet fund. A particular type of structured product that aims to deliver minimum returns, which usually are

at least equal to the sum invested, plus some additional upside based on the performance of the stock market. However, unlike guaranteed funds, very few floor funds come with a contractual guarantee. Many floor funds are managed using the technique of constant proportion portfolio insurance (CPPI).

FLOORTION

An option on a floor. The purchaser has the right, but not the obligation, to buy or sell a floor at a predetermined price on a predetermined date. See also caption

FORWARD

See future

FORWARD RATE AGREEMENT

A forward rate agreement (FRA) allows purchasers/sellers to fix the interest rate for a specified period in advance. One party pays fixed, the other an agreed variable rate. Maturities are generally out to two years and are priced off the underlying yield curve. The transaction is done 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’s maturity, the purchaser receives the difference 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 margin payments and the credit risk is limited to the mark-to-market value of the transactions. Unlike interest rate swaps, FRAs settle at the beginning of the interest period, two business days after the calculation date.

FORWARD START OPTION

An option that gives the purchaser the right to receive, after a specified time, a standard put or call option. The option’s strike price is set at the time the option is activated, rather than when it is purchased. The strike level is usually set at a certain fixed percentage in or out-of-the-money relative to the prevailing spot rate at the time the strike is activated.

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FORWARD SWAP

A swap in which rates are fixed before the start date. If a company expects rates to rise soon but only needs funds later, it may enter into a forward swap.

FRATION

See interest rate guarantee

FUTURE

A future is a contract to buy or sell a standard quantity of a given instrument, at an agreed price, on a given date. A future is similar to a forward contract and differs from an option in that both parties are obliged to abide by the transaction. Futures are traded on a range of underlying instruments including commodities, bonds, currencies and stock indexes. The most important difference between futures and forwards is that futures are almost always traded on an exchange and cleared by a clearing house, whereas forwards are over-the-counter instruments. Furthermore, futures, unlike forwards, have standard delivery dates and trading units. Most futures contracts expire on a quarterly basis. Contracts specify either physical delivery of the underlying instrument or cash settlement at expiry. Cash settlement involves the company paying or being paid the difference between the price struck at the outset and the expiry price of the contract. See also cost of carry, implied repo rate

FUTURE RATE AGREEMENT

See forward rate agreement

FUTURES OPTION

An option, either a put or a call, on any futures contract. Also known as an option on a future.

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GAMMA

The rate of change in the delta of an option for a small change in the underlying. The rate of change is greatest when an option is at-the-money and decreases as the price of the underlying moves further away from the strike price in either direction. A long gamma position is one in which a trader is long options. For a position that is short gamma, the opposite holds. Gamma can be hedged by mirroring the options position. Alternatively, a trader may choose to adjust the position in the underlying continually in order to maintain delta neutrality. See also vega

GARMAN-KOHLHAGEN MODEL

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

GEARED BARRIER OPTION

A type of in-the-money barrier option where the barrier is in-the-money and lies between the strike and the underlying spot rate.

GEARING

Gearing refers to the degree of exposure of a product to movements in the underlying index. A product with 100% gearing would have returns exactly equal to any rise in the index. A product’s gearing is also called participation.

GEOMETRIC BROWNIAN MOTION

Geometric Brownian motion is a model frequently used for the diffusion process followed by asset prices. Standard Brownian motion is a random walk process with Gaussian increments; that is, changes in the asset price are normally distributed. The term geometric means it is the proportional change in the asset price (as opposed to the absolute level) that is normally distributed. This gives the model useful properties, in that the asset price cannot be negative, and that the

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logarithm of the asset price will be normally distributed, making the model analytically tractable. See also stochastic process

GLOBAL FLOOR

A term usually associated with cliquet products. A cliquet product with global floor will provide a minimum return that is at least equal to the principal invested. Some cliquet products can have guaranteed principal redemption of more than 100%.

GROWTH PRODUCT

A term used to describe a type of structured product whose payouts are only made at maturity with no income stream during the product life. A growth product can be either principal guaranteed or non-guaranteed, although the former is common.

GUARANTEE LEVEL

The amount of principal that is guaranteed to be repaid at the maturity of the product.

GUARANTEED COUPON

Coupon payments that are guaranteed by the guarantor, and are paid during the life of the product irrespective of performance of the underlying.

GUARANTEED EXCHANGE RATE OPTION

An option (also known as a quanto option) on an asset in one currency denominated in a second currency. The exchange rate at which the purchaser converts the currency is fixed at the start. Such options are popular as investors want exposure to foreign assets without the foreign exchange risk. The extra cost of the option depends on the correlation between movements in the exchange rate and movements in the underlying. The higher (more positive) the correlation between the underlying and the exchange rate (expressed as the number of units of currency two per unit of currency one) the more expensive a call option will be and the cheaper a put option will be.

Quanto options can, however, look cosmetically cheaper (or more expensive) depending on the forward interest rates in the two currencies. For example, buying a call on a US asset could be more expensive in euros if there is a wide interest rate differential between the euro and the dollar. See also joint option, quanto product

GUARANTEED FUND

A guaranteed fund comes with a promise by the guarantor to repay a portion, usually 100% of the principal at maturity. Guaranteed funds can also incorporate guaranteed coupons payable regardless of the underlying performance and/or non-guaranteed coupons linked to the performance of underlying assets, often a stock index or basket of stocks.‘Guaranteed’ does not mean the investment is risk-free. The guarantee on principal repayment usually holds only when the product is held to maturity, and is subject to credit risk of the guarantor. Investors who redeem early are usually repaid at net asset value and thus subject to market risk. A guaranteed fund is constructed by investing part of the proceeds in a zero-coupon bond or other fixed income instrument – which underwrites the guaranteed payment at maturity – and the rest of the money in an embedded call or put option on the underlying for additional returns. Hence, investors also run counterparty risk in relation to the option strategy. A guaranteed structure can also take the form of a guaranteed note or guaranteed bond. Generally, any structured product with a promise to return 100% of the principal invested at maturity can be considered a guaranteed product.

GUARANTEED RETURN ON INVESTMENT

Any instrument (usually a structured note) which guarantees investors a minimum return on their investment. This can be achieved by combining a debt issue with a structure, such as a collar or cylinder, which locks gains into a range. This means that the investor gains protection from an adverse market move by limiting participation in any favourable move. See also principal-guaranteed product

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H

HAIRCUT

The excess of an asset’s market value over either the loan for which it can serve as adequate capital, or the regulatory capital value. It can also refer to the dealer’s commission on a transaction.

HARD PROTECTION

A term sometimes used to refer to the level of capital protection provided in a high-income type of structured product. A hard protection level of 90% means that so long as the index or basket of shares is above 90% of the starting level, the investor’s capital will not be at risk.

HEATH-JARROW-MORTON MODEL

A multi-factor interest rate model, which describes the dynamic of forward rate evolution. An extension of the Ho-Lee model, the underlying is the entire term structure of interest rates. The approach is very similar to the original Black-Scholes model: it does not model qualities such as the ‘price for risk’. The model requires two inputs: the initial yield curve and a volatility structure for the forward. The volatility is only specified in a very general form. By choosing an appropriate volatility function, it is possible to reduce HJM to simpler models such as Ho-Lee, Vasicek, and Cox-Ingersoll-Ross. The practical importance of the HJM model is that it provides a single coherent framework for pricing and hedging an entire book of instruments (including instruments such as caps and swaptions) and is not excessively computationally intensive. Research building on HJM (such as the market model) has concentrated on widening its scope to remove the possibility of negative interest rates, include more than one interest rate curve and incorporate default risk.

HEDGE

To hedge is to reduce risk by making transactions that reduce exposure to market fluctuations; for example, an

investor with a long equity position might compensate by buying put options to protect against a fall in equity 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 payments are above market rates. (Also known as a premium swap.)

HIGH-INCOME PRODUCT

A type of structured product that pays an income that is well above the rate of interest on conventional fixed-rate deposits. Generally, the higher the rate of return offered on a product, the higher the degree of risk.

HIGH-LOW OPTION

A combination of two lookback options. A high-low option pays the difference between the high and low of an underlying, such as a stock index. A speculative purchaser would be taking the view that the market would be more volatile than the implied volatilities of both lookback options incorporated in the structure. See also path-dependent option

HINDSIGHT OPTION

See lookback option

HISTORIC RATE ROLLOVER

A historic rate rollover allows an existing currency forward or spot position to be rolled forward without generating any intermediate cash flows. Effectively the position is reinstated for a new settlement date using a new off-market forward rate based on the historic rate.

HISTORICAL VOLATILITY

Historical volatility is a measure of the volatility of an underlying instrument over a past period. Historical volatility can be used as a guide to pricing options but isn’t necessarily a good indicator of future volatility. Volatility is normally expressed as the annualised standard deviation of the log relative return.

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HO-LEE MODEL

The first model that set out to model movements in the entire term structure 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 makes the simplifying assumption that the volatility structure remains constant along the yield curve. Heath-Jarrow-Morton later generalised this model, using a more general form of volatility and introducing continuous trading. In addition, Ho-Lee allows for the possibility of negative interest rates. The model was developed using a binomial tree, although closed-form solutions have now been found for discount bonds and discount bond options.

HULL-WHITE MODEL

An extension of the Vasicek model for interest rates, the main difference being that mean reversion is time-dependent. Both are one-factor models. The Hull-White model was developed using a trinomial lattice, although closed-form solutions for European-style options and bond prices are possible.

HYBRID PRODUCTS

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

HYPOTHECATION

The posting of collateral.

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IMPACT FORWARD

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

IMPLIED DISTRIBUTION

The probability distribution of returns for an asset, which is implied by options traded on that asset. The distribution is inferred by combining the variation of volatility with strike price (see volatility smile) and the assumptions made about the distribution in the option pricing model.

IMPLIED FORWARD CURVE

The forward curve implied by forward rate agreements (derived from the par curve) of various maturities. It is usually steeper than the spot yield curve.

IMPLIED REPO RATE

The return earned by buying a cheapest-to-deliver bond for a bond futures contract and selling it forward via the futures 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 higher vanilla option prices and vice versa. The effect of changes in volatility on an option’s price is known as vega. If an option’s premium is known, its implied volatility can be derived by inputting all the known factors into an option pricing model (the current price of the underlying, interest rates, the time to maturity and the strike price). The model will then calculate the volatility assumed in the option price, which will be the market’s best estimate of the future volatility of the underlying. See also option, volatility skew, volatility term structure

IN-ARREARS SWAP

See delayed reset swap

INCOME PRODUCT

A term used for any type of structured product that provides a periodic payment of income. The rate of income is often higher than the general rate of interest available on fixed-rate deposits and therefore there may be a risk the initial capital invested will not b returned in full.

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INDEX AMORTISING SWAP (IAS)

An interest rate swap whose principal amortises on the back of movements in an index, such as Libor or constant maturity treasuries. The fixed-rate receiver effectively grants an option to the fixed-rate payer to amortise the swap. The option is triggered by interest rate movements after an initial lock-out period. The notional principal amortises as rates fall or remains constant if rates remain the same. In return for granting the option, the fixed-rate receiver gets a yield above current fixed rates. IAS have been widely used by US regional banks in their asset/liability management activities. By using IAS, banks were able to obtain the negative convexity of a mortgage-backed security and avoid the risk of excessive prepayments due to changes in consumer sentiment. But the fixed receiver is exposed to both falling and rising rates. If rates fall, there is the possibility at each interest date that some or all of the swap will be terminated, creating a reinvestment risk. If rates rise, the swap may run to maturity, providing meagre income while floating rates soar. An IAS fixed-rate receiver is selling volatility to the payer for an enhanced yield. So the lower the volatility of the index, the lower the option value and yield pick-up. A subsequent fall in volatility benefits the receiver because the likelihood that the swap will amortise decreases. IAS can be structured with negative or positive convexity and the amortisation schedules and lock-out periods can be changed in order to increase or decrease yields. Also known as an Indexed principal swap. See also mortgage swap

INDEX ARBITRAGE

See stock index arbitrage

INDEXED STRIKE CAP

A cap for which the payout level is indexed to the level of the reference rate. For example, such a cap might be struck at 7.5% as long as the reference rate remained below 9%, but rise to 8.5% if the reference rate exceeded 9%. An indexed

strike cap is cheaper than a conventional cap.

INITIAL INDEX LEVEL

Most structured products incorporate payouts that are linked to the movement of an underlying index or share. This performance is measured relative to the level of the underlying recorded at the start of the investment term, or the initial index level.

INTEGRATED HEDGE

A hedge that combines more than one distinct price risk. For example, crude oil is usually priced in US dollars. Therefore a producer of crude oil whose home currency is not the dollar (say, the euro) is exposed to both currency risk and the price risk for crude oil. One possible integrated hedge would be a single quanto option, which would hedge the price of crude oil in euro. As such, it would depend heavily on the correlation (if any) between the two markets.

INTEREST RATE CORRIDOR

An interest rate corridor is composed of a long interest rate cap position and a short interest rate cap position. The buyer of the corridor purchases a cap with a lower strike while selling a second cap with a higher strike. The premium earned on the second cap then reduces the cost of the structure as a whole. The buyer of the corridor is protected from rates rising above the first cap’s strike, but exposed if they rise past the second cap’s strike. It is possible to limit this liability by selling a knock-out cap rather than a conventional cap. The structure is then known as a knock-out interest rate corridor.

INTEREST RATE GUARANTEE

An option on a forward rate agreement (FRA), also known as a FRAtion. Purchasers have the right, but not the obligation, to purchase an FRA at a predetermined strike. Caps and floors are strips of IRGs.

INTEREST RATE SWAP

An agreement to exchange net future cashflows. Interest rate swaps most commonly change the basis on which liabilities are paid on a specified principal.

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They are also used to transform the interest basis of assets. In its commonest form, the fixed-floating swap, one counterparty pays a fixed rate and the other pays a floating rate based on a reference rate, such as Libor. There is no exchange of principal – the interest rate payments are made on a notional amount. In floating-floating swaps the two counterparties pay a floating rate on a different index, such as three-month Libor versus six-month Libor. Swaps usually extend out as far as 10 years, although 12–40 year maturities are available in some liquid currencies. However, the longer the maturity of the swap, the less liquid it becomes and credit risk increases. Credit enhancements such as mutual put options and collateral are used to ameliorate the credit risk of longer term swaps. Interest rate swaps provide users with a way of hedging the effects of changing interest rates. For example, a company can convert floating-rate interest payments to fixed-rate payments if it thinks interest rates will rise (which would make its liabilities more expensive). Companies can also use interest rate swaps in conjunction with new debt issuance, raising money on, say, a fixed basis and swapping it into floating-rate debt. In an interest rate swap there is a fixed-rate payer (floating-rate receiver) and a fixed-rate receiver (floating-rate payer).

INTEREST-RATE CAP

See cap

IN-THE-MONEY

Describes an option whose strike price is advantageous compared with the current forward market price of the underlying. The more an option is in-the-money, the higher its intrinsic value and the more expensive it becomes. As an option becomes more in-the-money, its delta increases and it behaves more like the underlying in profit and loss terms; hence deep in-the-money options will have a delta of close to 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 the current forward market price. Option premiums comprise intrinsic value and time value.

INVERSE FLOATER

The payments made on an inverse floating rate note (‘floater’) decrease as the reference interest rate increases, the reverse of the typical case where the payments rise with the reference rate. The purchaser of an inverse floating rate note is in effect selling interest rate caps – this will increase the coupon payments in a stable or lower interest rate environment, but reduce them should interest rates rise. Typically, the payment is found by a fixed rate minus two times the reference rate. The floater can be further leveraged by using a multiplier higher than two.

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JOINT OPTION

An option on an underlying, often a stock index, denominated in a second currency. Unlike a guaranteed exchange rate option, in which exchange rates are fixed, the purchaser of a joint call option benefits from upside in the currency in which the asset is originally denominated, for example, S&P 500 call option struck in euro. In this case, at the inception, strike is specified in euro. At the maturity, S&P 500 level is observed and is multiplied by then current euro/US dollar rate. This converted value of S&P 500 is compared with the strike to determine the payout in euro. See also correlation, guaranteed exchange rate option, quanto product

JUMP DIFFUSION

One of the key assumptions of the Black-Scholes model is that the asset price follows geometric Brownian motion with constant volatility and interest 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

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used for modelling equities and emerging market currencies.

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KICKER

A kicker is a bonus payment that is sometimes made when a structured product matures if the value of the underlying asset has risen enough.

KNOCK-IN

Products which knock-in begin working when the underlying passes through a predetermined spot rate or barrier level. Knock-in options are a kind of barrier option.

KNOCK-OUT

Products which knock-out terminate when spot passes through a predetermined barrier level. Knock-out options are a kind of barrier option.

KNOCK-OUT INTEREST RATE CORRIDOR

A corridor in which a client purchases a standard cap with a lower strike and sells a knock-out cap with a higher strike (rather than selling a conventional cap). This means that the client is protected from an increase in interest rates up to the strike level for the knock-out cap, but exposed if rates rise beyond that level. However, the client is protected once again if the rates rise above the knock-out level, as the short knock-out cap will then be extinguished.

KURTOSIS

A measure of how fast the tails or wings of a probability distribution approach zero, evaluated relative to a normal distribution. The tails are either fat-tailed (leptokurtic) or thin-tailed (platykurtic). Markets are generally leptokurtic. The fatter the tails, the greater the chance a variable will reach an extreme value, implying that models such as Black-Scholes – which

assume perfect normal distribution – produce pricing biases for deep in- or out-of-the-money options.

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LADDER OPTION

A path-dependent option, most often based on an equity index or a foreign exchange rate. The payout of a ladder option increases stepwise as the underlying trades upwards (or downwards) through specified barrier levels (the ‘rungs’ of the ladder). Each time the underlying trades through a new barrier level, the option payout is locked-in at the higher level. See also cliquet, cliquet option, lookback option

LAMBDA

A measure of the effective leverage of an instrument. It is defined as the percentage change in the market value of a derivative for a one-percent move in the underlying. Unlike gearing, the lambda value captures the instrument’s delta. See also leverage

LEASE RATE SWAP

Similar to an interest rate swap, a lease rate swap is a fixed-for-floating agreement in which gold is borrowed/ lent at a "fixed" rate. The floating leg is re-priced at incremental time periods over the maturity of the swap. At the end of each floating period the agreed upon benchmark lease rate is compared to the contract rate and the party in debit pays the differential. The floating component is then rolled out for a further period.

LEGAL RISK

Legal risk arises from the risk of not legally being able to enforce contracts. It can be a particular issue in emerging markets where derivatives regulations are still being developed.

LEPTOKURTOSIS

See kurtosis

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LEVERAGE

The ability to control large amounts of an underlying variable for a small initial investment. Futures and options are regarded as leveraged products because the initial premium paid by the purchaser is generally much smaller than the nominal amount of the underlying. Leverage is usually measured as a quantity called lambda. See also lambda

LEVERAGED INVERSE FLOATER

See also inverse floater

LIBOR

The London inter-bank offered rate (LIBOR) is the interest rate charged on short-term interbank loans by banks operating in London. The rate is set on a daily basis and is commonly used as a guide for the future level of interest rates.

LIBOR-IN-ARREARS SWAP


LIMIT BINARY

See range binary

LINEAR BASKET CREDIT DEFAULT SWAP

A basket credit default swap, where investors are exposed to multiple reference entities as if they had entered into a separate credit default swap contract with respect to each reference entity.

LINEAR EX-LINKED SWAP

An interest rate swap with a quasi-fixed coupon that varies with the movement of a chosen spot foreign exchange rate over the life of the deal. These swaps can be structured to pay a higher (or lower) coupon if a given currency weakens (or strengthens) after the outset of the deal. The observation dates for the forex component coincide with the Libor reset dates for coupon calculation. These swaps can be structured with a leveraged forex exposure.

LIQUIDITY RISK

The risk associated with transactions made in illiquid markets. Such markets are characterised by wide bid/offer spreads, lack of transparency and large movements in price after a deal of any size. A firm wishing to unwind a portfolio of illiquid instruments (for example, highly tailored structured notes) may find it has to sell them at prices far below their fair values, exacerbating the problems that prompted the decision to unwind.

LISTED OPTION

See warrant, option

LITE OPTION

A European-style basket option with a payout determined by the underlying assets that remain in the basket, after a certain number of the best and worst performing assets in the basket were removed at a specified date prior to expiry. Also known as an atlas option.

LOCAL CAP

A local cap is the maximum return in each period of a cliquet option, which is used to work out the overall payout.

LOCAL FLOOR

A local floor is the minimum return in each period of a cliquet option, which is used to help work out the overall payout.

LONGSTAFF-SCHWARTZ MODEL

A two-factor model of the term structure of interest rates. It produces a closed-form solution for the price of zero coupon bonds and a quasi-closed-form solution for options on zero coupon bonds. The model is developed in a Cox-Ingersoll-Ross framework with short interest rates and their volatility as the two sources of uncertainty in the equation.

LOOKBACK OPTION

Lookback options give the holder the right at expiry to exercise the option at the most favourable rate or price reached by the underlying over the life of the option. As with average options, the strike may be either

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fixed or floating. With an optimal rate (or price) lookback option, the strike is fixed at the outset and the option will pay out against the highest (for a call) or lowest spot (for a put) reached over the life of the option, irrespective of the spot at expiry. The option will usually be settled in cash. Since the option is likely to have a larger payout than the corresponding plain vanilla option, it commands a larger premium. The strike for an optimal strike lookback option, on the 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’s life and exercised for cash or physical against the spot prevailing at expiry. See also cliquet option, ladder option, path-dependent option, shout option

LOW EXERCISE PRICE OPTION (LEPO)

A low exercise price option (Lepo) is a call option with an exercise price set deep in-the-money. The limiting case, a zero exercise price option, is when the strike price is zero. It is virtually certain to be exercised and the value and performance of its intrinsic value is effectively identical to that of the underlying equity. These features are designed to allow participation in the performance of an equity price where there are legal or financial obstacles to purchasing the underlying directly. If the Lepo is cash-settled, the buyer profits to the same extent as with a direct holding in the underlying, but without having to transact in it. However, a Lepo holder does not earn dividends or have voting rights over the equity.

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MANDARIN COLLAR

The Mandarin collar combines a range forward with the purchase of a range binary structure, such that should the spot stay within the prescribed range, the proceeds of the range forward are enhanced by the payout amount of the range binary. If either of the limits trades at any time, the range binary is terminated,

but the underlying exposure remains hedged by the range forward.

MARGRABE OPTION

See outperformance option

MARKET MODEL OF INTEREST RATES

A special case of the Heath-Jarrow-Morton model due to Brace, Gatarek and Musiela in which the term structure of interest rates is modelled in terms of simple Libor rates (which are lognormally distributed with respect to forward measure) rather than instantaneous forward rates. This allows the 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 readily available market data: forward or swap rates volatilities and correlations, and is particularly suited to path-dependent instruments.

MARKET RISK

Exposure to a change in the value of some market variable, such as interest rates or foreign exchange rates, equity or commodity prices. For holders of a derivatives position, market risk may be passed through from a change in the value of the underlying to the price of the derivatives, or may arise from other sources, such as implied volatility or time decay.

MARKET VALUE

See replacement cost

MARK-TO-MARKET

This is the value of a financial instrument according to current market rates.

MARTINGALE

A probabilistic interpretation of the payout of a ‘fair game.’ The expected gain at any point in the future is equal to the actual gain now. See also stochastic 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

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tendency is one explanation for the behaviour of the term structure of volatility. Some interest rate models incorporate mean reversion, such as Vasicek 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 instrument with a maturity of between three and seven years, which may pay fixed or variable coupons. These notes can be used to construct structured notes by embedding derivatives to create structured coupons which appeal to investors.

MID-ATLANTIC OPTION

See Bermudan option

MONTE CARLO SIMULATION

A method of determining the value of a derivative by simulating the evolution of the underlying variable(s) many times over. The discounted average outcome of the simulation gives an approximation of the derivative’s value. This method may be used to value complex derivatives, particularly path-dependent options, for which closed-form solutions have not been or cannot be found. Monte Carlo simulation can also be used to estimate the value-at-risk (VaR) of a portfolio. In this case, a simulation of many correlated market movements is generated for the markets to which the portfolio is exposed, and the positions in the portfolio revalued repeatedly in accordance with the simulated scenarios. The result of this calculation will be a probability distribution of portfolio gains and losses from which the VaR can be determined. The principal difficulty with Monte Carlo VaR analysis is that it can be very computationally intensive.

MORTGAGE SWAP

An asset swap attached to fixed-rate mortgage payments. Mortgage swaps allow investors to enjoy the flows from a portfolio of mortgages without taking a mortgage asset on to their balance sheet. The principal reduces if and when the outstanding mortgage principal reduces

(which can occur if the mortgage holder pays off the mortgage or defaults). Such swaps are complicated because although the fixed-rate receiver receives a higher rate than on a normal swap, the amortisation of the principal is not just a function of interest rates. The largest mortgage swap market is in the US; in 1992 and 1993 prepayments accelerated because of historically low interest rates. See also index amortising swap, reverse index amortising swap

MORTGAGE-BACKED SECURITY

See 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 the next period at the current interest rate plus a pre-agreed spread. See also cliquet option

MULTI-FACTOR MODEL

Any model in which there are two or more uncertain parameters in the option price (one-factor models incorporate only one cause of uncertainty: the future price). Multi-factor models are useful for two main reasons. Firstly, they permit more realistic modelling, particularly of interest rates, although they are very difficult to compute. Secondly, multi-factor options (for example, spread options) have several parameters, each with independent volatilities, and also the correlation between the underlyings must be dealt with separately.

MULTIPLE STRIKE OPTION


MUNICIPAL SWAP

A swap in which the floating payments are based on an index of tax-exempt US municipal bonds, such as J.J. Kenny.

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NAKED OPTION

An option that is sold (bought) without holding the underlying or otherwise hedging.

NATURAL HEDGE

A natural hedge is the reduction in financial risk that can arise from an institution’s normal operating procedures. For instance, a company that has a significant portion of its sales in one country will have a natural hedge to at least part of its currency risk if it also has operations in that country generating expenses in the currency. Firms may act to increase natural hedges by changing sourcing, funding, or operational decisions, but natural hedges are less flexible, and more difficult to reverse, than financial hedges.

NEGATIVE BASIS

Negative basis exists when the cost of buying protection (in the credit derivatives market) on a particular reference entity is less than the credit spread (generally expressed as a spread to Libor) on a bond or note of similar maturity issued by that reference entity. When this occurs, investors can lock in riskless profit by buying bonds and buying credit protection. These arbitrage opportunities are generally only available to investors whose cost of funds is Libor flat or better (since funding the bond or note at Libor plus a spread will erode the arbitrage). Technical factors between the bond and credit derivatives market account for negative basis.

NET PRESENT VALUE

A technique for assessing the worth of future payments by looking at the present value of those future cashflows discounted at today’s cost of capital.

NON-DELIVERABLE FORWARD

Non-deliverable forward contracts (NDFs) – also called dollar-settled forwards – are

synthetic forwards, which entail no exchange of currencies at maturity. Instead, settlement is made in US dollars based on the difference between the agreed contract rate at inception and a market reference rate at maturity. NDFs can be used to establish a hedge or take a position in one of a growing group of emerging market currencies where conventional forward markets either do not exist or may be closed to non-residents. As offshore instruments, NDFs offer the advantage of eliminating convertibility risk, since no emerging market currencies are exchanged at maturity.

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ONE-FACTOR MODEL

A model or description of a system where the model incorporates only one variable or uncertainty: the future price. These are simple models, usually leading to closed-form solutions, such as the Black-Scholes model or the Vasicek model.

OPEN-ENDED PRODUCT

Structured products that can be used for investment for an unlimited period are sometimes called open-ended products. They stand in contrast to tranche or close-ended products.

OPERATIONAL RISK

The risk run by a firm that its internal practices, policies and systems are not rigorous or sophisticated enough to cope with untoward market conditions or human or technological errors. Although operational risk is not as easy to identify or quantify as market or credit risk, it has been implicated as a major factor in many of the highly-publicised derivatives losses of recent years. Sources of operational risk include: failure to correctly measure or report risk; lack of controls to prevent unauthorised or inappropriate transactions being made (the so-called ‘rogue trader’ syndrome); and lack of understanding or awareness among key staff.

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OPTION

A contract that gives the purchaser the right, but not the obligation, to buy or sell an underlying at a certain price (the exercise, or strike price) on or before an agreed date (the exercise period). For this right, the purchaser pays a premium to the seller. The seller (writer) of an option has a duty to buy or sell at the strike price, should the purchaser exercise his right. With European-style options, purchasers may take delivery of the underlying only at the end of the option’s life. American-style options may be exercised, for immediate delivery, at any time over the life of the option. Holders of semi-American-style or Bermudan options may be exercised on specified dates – typically on a monthly or quarterly basis. Options can be bought on commodities, stocks, stock indexes, interest rates, bonds, currencies, etc. The trading terminology, though, may change according to the product. In most cases, the right to buy the underlying is known as a call, and the right to sell, a put. Options are traded on formal exchanges and in over-the-counter (OTC) markets. The exchanges, such as the Hong Kong Stock Exchange, the SIMEX, or the ASX provide primarily standardised options; the OTC markets are able to provide tailored products to fit specific requirements. The choice between OTC and exchange-traded options will depend on the degree of tailoring required, the relative liquidity of both markets (this varies greatly according to the underlying) and credit concerns. Pricing models for simple or vanilla options have five major inputs: the option’s exercise or strike price; the time to expiration; the price of the underlying instrument; the risk-free interest rate on the underlying instrument, and the volatility of the underlying instrument. European-style options are usually priced off a closed-form analytical model first published by Fischer Black and Myron Scholes in 1973, which has subsequently been modified to fit different underlying. At maturity, an option’s value will depend on the value of the right to buy or sell a product. If an option is purchased giving the right to buy gold at $375 an ounce and at expiration the rice is $400, the option is worth $25.

The extent to which an option is in-the-money (how far the strike price is below/above the current forward market price) is called its intrinsic value. Where the strike price is less favourable than the market price, the option is said to be out-of-the-money, and where the two prices are the same it is at-the-money. At any time before maturity, an option’s price will be a combination of its intrinsic value (which is always either greater than, or equal to, zero) and its time value. The latter includes the cost of carry and the probability that the price of the underlying will move into or remain in the money. Options can broadly be used in two ways – for speculation, or for insurance. Their usefulness, both from a buyer’s and a seller’s point of view, derives from their payouts. In contrast to other types of hedge, options provide insurance against unfavourable moves in a product’s price and the opportunity to take advantage of favourable moves. Forwards and futures, for example, require buyers and sellers to lock into one rate. In return for assuming this risk, sellers of options receive a premium, effectively a risk-taking fee. The payout of a purchased option means that the price risk of an option is limited to its premium – it is not as exposed to adverse movements as a position in the underlying. For speculators selling (writing) options, this often means taking a naked option position and therefore being exposed to adverse movements in the underlying. Hedgers may sell options to garner premium to offset any expected slight downturn in a market. Since option premiums are only a fraction of the cost of the underlying product, it is possible to achieve a much greater exposure to price changes of the underlying compared with a similar investment directly in the product – this is called leverage. See also implied volatility

OPTION COMBINATION STRATEGIES

Options may be combined so that their payouts produce a desired risk profile. Some combinations are primarily trading strategies, but option combinations can be useful in, for example, allowing investors to construct a strategy to take advantage of a particular view they have of the market. Other strategies allow purchasers to reduce their premiums by giving up some of the benefits they may have received from market

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movements. See also put spread, straddle, strangle

OPTION ON FUTURE

See futures option

OPTION REPLICATION

See replication

OPTION STYLES

The purchaser of a European-style option has the right to exercise it on a predetermined expiry date. In contrast, the holder of an American-style option has the right to exercise it at any time during its lifetime, up to and including its expiry date. This flexibility means there is a greater probability of an American-style option being exercised than the corresponding European-style option with the same strike. Hence the early exercise feature of an American option adds value and makes it the more expensive of the two. Most exchange-traded options are American-style. Further variations on these styles also exist. A Bermudan option, so called because it falls between American- and European-style options, has more than one possible exercise date. For example, the holder of a Bermudan option with a two-year maturity might have the right to exercise it every quarter or half year during the life of the contract. Bermudans are also known as limited exercise or semi-American-style options. Another twist is the deferred payout option, a variation on American-style options in which the option can be exercised at any time during the option’s life, but the payout is delayed until the expiry date.With the similar shout option, the purchaser can lock in a profit at any time, but retains the right to profit from further favourable moves. See also American-style option, Bermudan option, deferred payout option

OUT-OF-THE-MONEY

Describes an option for which the forward market price of the underlying is below the strike price in the case of a call, or above it in the case of a put. The more the option is out-of-the-money, the cheaper it is (since the chances of it being exercised get

slimmer). Its delta also declines and it becomes less sensitive to movements in the underlying. See also at-the-money, in-the-money

OUTPERFORMANCE OPTION

Also known as a Margrabe option. A two-factor option giving the purchaser the right to receive the outperformance of one asset over another asset. For example, a purchaser with a view that the Hang Seng Index (HSI) will outperform the Dow Jones Euro Stoxx 50 (Euro Stoxx) index should buy the outperformance option, which pays notional multiplied by the outperformance of the HSI index over the Euro Stoxx index. In this case, the payout is zero if HSI underperforms Euro Stoxx. The value of an outperformance option will largely be dictated by the historical correlation between the underlyings.

OVERLAY

A strategy to change the exposure of a portfolio using derivatives, while leaving the securities in the underlying portfolio unchanged. This has the advantage of cost and flexibility, as portfolio managers can adjust portfolio risk more quickly and cheaply with derivatives than by liquidating portfolio holdings. Another reason might be tactical – the adjustment may only be desired for a brief period of perceived market threat. A third reason might be to transform a portfolio risk; an international fund manager may wish to segregate the currency aspect of a portfolio and can do so with a currency overlay programme. See also asset allocation

OVER-THE-COUNTER (OTC)

Financial products that are not traded on formal exchanges are said to be traded over-the-counter.

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PARISIAN BARRIER OPTION

A barrier option with a barrier that is triggered only if the underlying has been beyond the barrier level for longer than a specified period

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of time. See also barrier option, trigger, trigger condition

PARTICIPATING FORWARD

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

PARTICIPATING OPTION

An option whereby the buyer pays a reduced premium but has to forgo a portion of his potential gains.

PARTICIPATING SWAP

A swap in which floating-rate exposure is hedged but in which the hedger still retains some benefit from a fall in rates.

PARTICIPATION RATE

Many structured products incorporate returns at maturity that are calculated by multiplying the performance of the underlying (which can be an index, stock basket or fund) by a fixed percentage. This percentage is called the participation rate. For example, a 70% participation in the index means that 70% of the performance of the underlying index will be used to calculate the maturity payout. If the product comes with a 100% capital guarantee, the participation rate will only apply to the upside, not to index losses.

PATH-DEPENDENT OPTION

A path-dependent option has a payout directly related to movements in the price of the underlying during the option’s life. By contrast, the payout of a standard European-style option is determined solely by the price at expiry. See also barrier option, cliquet option, high-low option, lookback option, shout option

PAY-AS-YOU-GO CAP

A pay-as-you-go cap allows the buyer to pay for protection from upward moves in an interest rate for only as long as

necessary. Usually, the holder will pay an initial premium (which will be small compared with the premium for a normal cap) and a further payment at each reset date. The holder can cancel the cap when he or she feels that the protection is no longer needed. A pay-as-you-go cap is useful for those who feel that caps are too expensive, that interest rates will eventually stabilise below the capped level, or that rates are in a short-lived ‘spike’ move. Also known as an installment cap.

PAYOUT/PAYOFF

A general term used to describe the return provided by a structured product or an option. A lot of products pay a fixed coupon plus additional returns linked to performance of the nderlying. If the embedded option is path-dependent, the returns will be a function of both the performance of the index and the payout formula. For example, the payout from a five-year quarterly Asian option with a 70% participation of the Dow Jones Euro Stoxx 50 Index is equal to 70% of the average of 20 different prices over five years, and not the level of the index at maturity.

PERIOD RESETTING SWAP

An interest rate swap in which the floating-rate payments are an average of the floating rates observed since the last payment.

PERIODIC CAP

A cap in which the strike rate can vary from period to period. The strike rate in a given period depends upon the strike set in the previous period. Such caps are normally set at a fixed number of basis points above the previous strike, or the index (for example, Libor) plus a spread. Periodic caps can be with or without "memory". A periodic cap without memory simply looks at the strike in the immediately preceding period to determine a new strike, while one with memory may look at previous settings in determining the new strike. Periodic caps are common features in adjustable rate mortgages (ARMs) in the US where the borrower’s floating interest payments cannot go up by more than a set number of basis points in a given year. See also periodic floor

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PERIODIC FLOOR

A floor in which the strike rate can vary from period to period. The strike rate in a given period depends upon the strike set in the previous period. Such floors are normally set at a fixed number of basis points above the previous strike or the index (for example Libor) plus a spread. See also periodic cap

PIN RISK

The phenomenon where a small move in the underlying can have a significant impact on the value of an at-the-money option shortly before expiration.

PODIUM

A type of correlation product that is fully capital-guaranteed, but with the annual coupons dependent upon the number of underlyings within the basket that meet certain performance criteria.

PORTFOLIO OPTION

A portfolio option is a multi-factor option that pays out the difference between the return from a portfolio of assets and a specified strike price.

POSITIVE BASIS

Positive basis exists when the cost of buying protection (in the credit derivatives market) on a particular reference entity exceeds the credit spread (generally expressed as a spread to Libor) on a bond or note of similar maturity issued by that reference entity. When this occurs, investors looking to gain exposure to the reference entity can improve their expected return on an investment by taking exposure to the credit by selling protection in the credit derivatives market rather than buying the bond or note. Technical factors between the bond and credit derivatives market account for positive basis.

POWER OPTION

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

POWER SWAP

A swap whose floating leg is based on the square (or some higher exponent) of the reference interest rate. Although dismissed by some as little more than a speculative tool for taking highly leveraged positions on the direction of interest rates, power swaps have been shown (by Robert Jarrow and Donald van Deventer) to have their uses in hedging commercial banks’ deposits and credit card loan portfolios. See also power option

PREMIUM

See option

PREMIUM-REDUCTION DEVICE

A strategy that aims to reduce the cost of an option or other derivative. There are many ways to achieve this; three common techniques follow. The first is to sell a second derivative; the premium received can then be used to lower the funding requirement for the purchased derivative. This is the technique employed for reducing the cost of a collar. The second is to limit participation in moves in the underlying by imposing limitations on the payout profile of the instrument (as in a barrier option or a capped floater). The final way is to accept payments below market rates, with the possibility of making up the shortfall at the end of the instrument’s life (see yield adjustment).

PRINCIPAL-GUARANTEED PRODUCT

Any investment vehicle that allows investors to gain exposure to an asset while guaranteeing the return of their principal, often at maturity only. Such products are normally constructed by buying a deep discount bond (often a zero-coupon bond) and using the rest of the money to buy embedded call or put options to gain exposure to a second asset, often a stock index. See also guaranteed return on investment

PROGRAM TRADING

A strategy to trade a basket of shares simultaneously, normally by means of computer-generated instructions. Where the asset class is considered more important than the selection within that class, program

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trading (also known as basket trading) is used to lower trading costs since trading a basket of shares is cheaper than buying or selling those shares individually. Program trading is different from stock index arbitrage, although it is used in such a strategy.

PROMPT

For immediate (ie, two days) delivery.

PROTECTION LEVEL

This refers to the safety level of the underlying at which the investor can still keep their capital intact. Once this level is breached, the original investment amount is at risk.

PUT OPTION

See option Put spread A put spread reduces the cost of buying a put option by selling another put at a lower level. This limits the amount the purchaser can gain if the underlying goes down, but the premium received from selling an out-of-the money put partly finances the at-the-money put. A put spread may also be useful if the purchaser thinks there is only limited downside in the market. See also call spread, option combination strategies

PUT-CALL PARITY

The relationship between a European-style put option and a European-style call option on the same underlying with the same exercise price and maturity. Put-call parity states that the payout profile of a portfolio containing an asset plus a put option is identical to that of a portfolio containing a call option of the same strike on that same asset (with the rest of the money earning the risk-free rate of return). In practice, a put option on, say, a stock index, can be constructed by shorting the stock and buying a call option. The relationship means that traders are able to arbitrage mispriced options. See also reversal

PUTTABLE SWAP

An interest rate swap in which the fixed-rate receiver has the right to terminate the contract after a specified period. The puttable swap is the opposite of a callable swap. The fixed-rate payer is effectively sold a swaption, who receives a lower fixed rate in compensation. Puttable swaps are similar to extendible swaps. Also known as a cancellable swap.

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QUANTO PRODUCT

An asset or liability denominated in a currency other than that in which it is usually traded, typically equity index futures, equity index options, bond options and interest rate swaps (differential swaps). Quanto products can be hedged with an offsetting position in a local currency product. Variable asset and foreign exchange exposures will arise with changes in the foreign exchange rate and in the underlying, so the structures must be continually dynamically hedged in a similar fashion to option products. See also guaranteed exchange rate option, joint option

QUANTO SWAP

Also called a differential swap. A quanto swap is a fixed-floating or floating-floating interest rate swap. One of the floating rates is a foreign interest rate, but is applied to a notional amount denominated in the domestic currency. For example, a US investor may enter into a five-year swap in which he makes payments in US dollars at the six-month USD Libor plus a spread semi-annually, and receives payments in US dollar at JPY Libor. The payments are calculated by applying the respective interest rates to a notional amount of US$100 million. However, the notional principal can also be denominated in the Japanese yen, or in a third currency such as the British pound. A quanto swap enables the investor to avoid exchange rate risk while taking advantage of interest rate differentials. A corporate borrower with debt in a discount currency can use a quanto swap to lower his borrowing costs, while portfolio managers

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can use a quanto swap to enhance yield with higher interest rates in a discount currency.

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RAINBOW OPTION

Similar to a multi-factor option. It is an option with the payout linked to two or more underlying instruments or indexes. Some common types of rainbow options are the maximum option, minimum option, best-of option and worst-of option. The underlyings are of the same asset class and can have different expiry dates and strike prices, but for the option to payout, all the underlyings must move in the direction that is favourable to the option holder. However, if the option combines two or more types of asset classes, such as a stock index and an exchange rate, it is called a hybrid option.

RANDOM WALK

The series of values taken by a random variable with the progress of some parameter such as time. Each new value (each new step in the walk) is selected randomly and describes the path taken by the underlying variable. See also stochastic process

RANGE ACCRUAL OPTION

An option that pays out a fixed amount at expiration for each day that the index rate remains within the specified range.

RANGE BINARY

The range binary structure has been developed primarily for trading purposes and is essentially a bet on a spot staying within a given range. The strategy is often linked with a deposit for yield enhancement purposes. A range is specified by the customer over a fixed period. A premium is paid up front and provided that the spot stays within the range (as monitored on a 24-hour basis), then a multiple of the premium invested will be payable. A rebate range binary is

one in which the premium invested is rebated if a designated boundary of the range is breached first. A similar structure, the limit binary, is also essentially for trading. This is fundamentally a bet on a spot not staying within a predetermined range. The customer specifies two spot rates, one above and one below the current spot rate. A premium is paid up front, and providing that both levels trade (as monitored on a 24-hour basis), a fixed multiple of the premium invested will be payable. See also trigger condition

RANGE NOTE

A range note (also known as a fairway note, an accrual note, or a corridor floater) is a structured note, which pays a coupon for each day that the underlying spot stays within a specified range (sometimes called the accrual corridor). If the underlying trades outside the specified range, the investor receives no interest for that day. The underlying can be a reference interest rate, a foreign exchange rate, an equity price or the spread between two interest rates. The range is determined at the outset to suit the investor’s risk/return requirements, but might also be reset by the investor or be automatically centred on the prevailing rate at each reset date. This higher yield is achieved by the investor selling an embedded corridor option, particularly in times of high volatility. The holder of the note will therefore benefit in stable market periods when volatility is low.

RANGE RESETTABLE FORWARD

A type of forward contract that offers a more favourable forward rate compared with an ordinary forward, as long as the spot rate remains within a pre-defined range.

RATCHET FLOATER

Also called a one-way floating rate note. A ratchet floater is a structured note that pays a floating interest rate indexed on a reference rate such as Libor. Each floating interest rate will depend on the previous interest rate paid.

RATCHET OPTION

See cliquet option

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RATIO CALENDAR SPREAD

A strategy that involves the purchase of a long-term option (either call or put) and the selling of a greater amount of near-term option at the same strike price.

REBATE

Barrier options often have a rebate associated with the trigger level(s). A rebate is an amount paid to the holder of the derivative if the instrument is knocked-out or is never activated during its lifetime as partial recompense for their initial investment. One example is the rebate range binary. Regulatory arbitrage A financial transaction that allows one or both of the counterparties to accomplish an operating or financial objective that would be unavailable to them directly because of regulations: for example, a commercial bank entering into a credit default swap with an OECD bank in order to lower the regulatory capital that it must hold.

REGULATORY CAPITAL

The amount of capital that an organisation is required to hold by its regulator.

REINVESTMENT RISK

The risk that an asset manager will be unable to match the yield from an interest-rate instrument (such as a swap or bond) when reinvesting its coupon payments and principal repayments.

RELATIVE PERFORMANCE OPTION


RELATIVE PERFORMANCE RISK

The risk that a fund manager’s choice of investments will fail to match the performance of the benchmark against which the fund is measured, prompting fund redemptions. A similar risk is run by corporate treasury risk managers who are measured against benchmark hedge levels. One way to address this type of risk is with outperformance options. Relative performance risk is also used to refer to the risk that an individual asset will underperform relative to its asset class.

For equities, this may be measured by a stock’s beta, its standardised covariance with respect to the relevant equity index. See also specific risk

REPLACEMENT COST

Often used in terms of credit exposure, the replacement cost of a financial instrument is its current value in the market – in other words, what it would cost to replace a given contract if the counterparty to the contract defaulted. Aside from bid-ask conventions, it is synonymous with market value.

REPLICATION

To replicate the payout of an option by buying or selling other instruments. Creating a synthetic option in this way is always possible in a complete market. In the case of dynamic replication this involves dynamically buying or selling the underlying (or normally, because of cheaper transaction costs, futures) in proportion to an option’s delta. In the case of static replication the option (usually an exotic option) is hedged with a basket of standard options whose composition does not change with time – eg, an at-expiry digital option can be replicated with a call spread. See also static replication, synthetic asset

REPO AGREEMENT

To buy (sell) a security while at the same time agreeing to sell (buy) the same security at a predetermined future date. The price at which the reverse transaction takes place sets the interest rate over the period (the repo rate). The most active repo market is in the US, where the Federal Reserve sets short-term interest rates by lending securities. In a reverse repo the buyer sells cash in exchange for a security. Repos can benefit both parties. Buyers of repos often receive a better return than that available on equivalent money-market instruments; and financial institutions, particularly dealers, are able to get sub-Libor funding. A slight variation on the repo is the buy/sell back. The buy/sell back’s coupon becomes the property of the purchaser for the duration of the agreement. It is preferred by credit-sensitive investors such as central banks.

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REPO RATE

See repo agreement

RESET-IN-ARREARS SWAP


RESETTABLE CONVERTIBLE BOND

It is a convertible bond where the conversion ratio can reset to a new value depending on the average price of the underlying stock on pre-specified dates. See also convertible bond

REVERSAL

To take advantage of mispriced options by creating a synthetic long futures position and edging it by selling futures contracts against it. A trader may buy an undervalued call, at the same time selling a fairly valued put and buying a futures contract. The same strategy could be applied if the put was undervalued. The ability to undertake this riskless arbitrage relies on put-call parity. See also convergence trade, put-call parity

REVERSE BARRIER OPTION

See barrier option

REVERSE CASH-AND-CARRY ARBITRAGE

A technique, used mainly in bond futures and stock index futures, that involves buying a futures contract and selling the underlying. It is used when a futures contract is theoretically cheap, such as when the implied repo rate is less than the market repo rate. See also cash-and-carry arbitrage

REVERSE CONVERTIBLE

These are just like convertible bonds. The main difference is that rather than buying a call option on a stock, the investor sells a put on the stock or index. The investor receives higher than normal coupons but may lose some principal if the put ends up in the money.

REVERSE INDEX AMORTISING SWAP

An interest rate swap in which payments are linked to an index (eg, Libor or

constant maturity Treasuries) and increase if that index declines. The swap therefore exhibits positive convexity. Receiving fixed in a reverse index amortising swap (reverse IAS) provides a hedge for instruments (such as mortgage swaps) that amortise as interest rates decline, although it is important to ensure that the indexes on which the amortisation or accreting schedules are based are highly correlated. Unlike a conventional IAS, the fixed receiver of a reverse IAS is buying volatility (sometimes referred to as ‘optionality’) which offsets the short option position of a mortgage portfolio. See also mortgage swap

REVERSIBLE SWAP

An interest rate swap in which one side has an option to alter the payment basis (fixed/floating) after a certain period. This is usually achieved by the use of a swaption, allowing the purchaser the opportunity to enter a swap with payment on the opposite basis. The swaption would be for twice the principal amount, one half nullifying the original swap.

RHO

Measures an option’s sensitivity to a change in interest rates. This will have an impact on both the future price of the option and the time value of the premium. Its impact increases with the maturity of the option.

RISK NEUTRAL VALUATION

An argument that underpins most derivatives pricing, including the Black-Scholes model. The differential equation describing the price of a derivative does not involve parameters that depend on risk preferences. Derivatives prices in a market where all investors are risk neutral must therefore be the same as prices in the real world and this corollary considerably simplifies model construction.

RISK REVERSAL

The term ‘risk reversal’ is also used, by currency option traders, to denote the difference in implied volatility between out-of-the-money call and put options, which both have a delta of 25%. The level of the risk reversal is often used as a sentiment indicator in currency markets as it indicates

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the relative demand for calls versus puts. See also collar, volatility skew

ROLLER-COASTER SWAP

An interest rate swap in which one counterparty alternates between paying fixed and paying floating. Another name for a seasonal swap.

ROLL-OVER RISK

The risk that a derivatives hedge position will be at a loss at expiry, necessitating a cash payment when the expiring hedge is replaced with a new one. Normally, such a roll-over loss simply represents an opportunity loss, but sometimes the cash cost is consequential.

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SEASONAL SWAP

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

SECURITISATION

The conversion of assets (usually forms of debt) into securities, which can be traded more freely and cheaply than the underlying assets and generate better returns than if the assets were used as collateral for a loan. One example is the mortgage-backed security, which pools illiquid individual mortgages into a single tradable asset.

SEMI-FIXED SWAP

An interest rate swap with two possible fixed rates, which can be tailored to suit bullish or bearish market views. The rate paid by the fixed-rate payer depends on whether current Libor (or another reference rate or asset) is above or below a predetermined level. In a typical structure, if Libor is below the trigger level, the lower of the two rates is paid, if it is

above, the higher is paid. These swaps can be used to create asymmetric risk exposures, ie, cheaper fixed-rate funding for an oil producer when oil prices are low, or an enhanced yield for an insurance company when equity prices are falling.

SETTLEMENT RISK

Settlement risk (delivery risk), as a particular form of counterparty credit risk, arises from a non-simultaneous exchange of payments. For example, a bank that makes a payment to a counterparty, but will not be recompensed until a later date, is exposed to the risk that the counterparty may default before making the counter-payment. Settlement risk is distinct from market risk because it relates to exposure to a counterparty rather than exposure to the underlying risk related to the reference entity of the derivatives contract.

SHOUT OPTION

A type of path-dependent option that allows the investor to lock in profits if he thinks the market has reached a high (for a call) or low (for a put). The investor benefits further if the market finishes higher or lower than the shout level. The shout option is designed for investors who have a directional view on the market and want to take positions, but are worried about the volatility of the asset and want to lock in a minimum return. See also lookback option, path-dependent option

SKEW

A skewed distribution is one that is asymmetric. Skew is a measure of this asymmetry. A perfectly symmetrical distribution has zero skew, whereas a distribution with positive (negative) skew is one where outliers above (below) the mean are more probable. An example of an asymmetric distribution in the financial markets is the distribution implied by the presence of a volatility skew between out-of-the-money call and put options.

SPECIFIC RISK

Specific risk, also known as non-systematic risk, represents the price variability of a security that is due to factors unique to that security, as opposed to that portion that is

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due to systematic risk, the generalised price variability of the related interest rate or equity market. As an example, a US Treasury note would have no specific risk, as it is deemed to have no risk other than movement in interest rates, while a corporate bond would have a degree of default risk as well as more generalised yield curve risk. See also relative performance risk

SPREAD OPTION

The underlying for a spread option is the price differential between two assets (a difference option) or the same asset at different times or places. An example of a financial difference option is the credit spread option, the underlying for which is the spread between two debt issues, which derives from the relative credit rating of the issuers. Another is the cross-currency cap, where the underlying is the spread between interest rates in two different currencies. A calendar spread, a pair of options with the same strike price but different maturities, pays out the price difference for a single asset on two different dates. Spread options, including calendar spreads, are particularly popular in the commodity markets.

SPREAD-LOCK SWAP

An interest rate swap in which one payment stream is referenced at a fixed spread over a benchmark rate such as US Treasuries.

SQUEEZE

Pressure on a particular delivery date resulting in making the price of that date higher relative to other delivery dates.

STATIC REPLICATION

Static replication is a method of hedging an options position with a position in standard options whose composition does not change through time. The method attempts to replicate the payout of the instrument in a more manageable fashion than dynamic replication, where a position in the underlying or futures contracts must be dynamically adjusted if it is to remain effective. Because it uses options to

hedge options, a static replication portfolio is a better hedge for gamma and volatility, as well as delta, than dynamic replication. Static replication can be used for hedging a position in exotic options with vanilla options, or for replicating a long-term option with short-term options. In practice, however, it is not always possible to hedge using static replication. The number of different options and notional amounts required can quickly become unmanageable. See also delta-hedging, replication, synthetic asset

STATISTICAL ARBITRAGE

In the mid-1980s it was discovered that exhibit autocorrelations – implying that earlier price changes could be used to forecast future changes. Statistical arbitrageurs seek to exploit these patterns in their trading strategies.

STEP-DOWN SWAP

The opposite of an escalating rate swap; ie, the fixed rate decreases in increments over the life of the swap

STEP-UP SWAP

See accreting

STEP-UP/DOWN RANGE FORWARD

A self-adjusting range forward structure, which is particularly suitable for hedging purposes. If the strike level of the long put option is breached, the strike automatically adjusts up or down (according to exposure) to a new, more favourable, level. Stochastic optimisation model A model or description of a system in which the choice of action that can be taken is dependent on the values of some random variables. For example, the value of an American-style option is such that the best choice of exercise is always made.

STOCHASTIC PROCESS

Formally, a process that can be described by the evolution of some random variable over some parameter, which may be either discrete or continuous. Geometric Brownian motion is an example of a stochastic process parameterised by time. Stochastic processes are used in finance to develop models of the future price of an instrument in terms of the

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spot price and some random variable; or analogously, the future value of an interest or foreign exchange rate. See also Geometric Brownian motion, martingale, random walk

STOCHASTIC VOLATILITY

One of the key assumptions of the Black-Scholes model is that the stock price follows geometric Brownian motion with constant volatility and interest 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 longer describes a complete market, since there is now another source of uncertainty in the option pricing model. A variety of approaches have been attempted to resolve this difficulty since the mid-1980s, most notably the Heath-Jarrow-Morton framework.

STOCK INDEX ARBITRAGE

The technique of selling a futures contract on a stock index and buying the underlying stocks, via programme trading, or vice versa when the price of the futures contract is above or below its theoretical value. The ability to conduct such strategies depends on the efficiency of the futures and cash markets.

STOCK INDEX FUTURE

A futures contract on a stock index. Most are cash-settled. The theoretical price of a stock index future equals the cost of carrying the underlying stock for that period: the opportunity cost of the funds invested minus any dividends. If the cost of buying and holding the underlying stocks is less than the futures price, an arbitrageur can sell futures and buy the underlying stocks. The higher interest rates are (compared with the dividend yield), the greater the opportunity cost of holding the stocks, hence the futures price should be higher than the current index price. If interest rates are less than the dividend yield, the opportunity cost of holding stocks is less and the futures price should fall below the current index price. There is usually a so-called arbitrage band in which, although

the futures and underlying prices diverge, it is not worthwhile arbitraging the two. This arises as a result of transaction costs from bid-ask spreads, the market impact of buying and selling stock, and execution risks.

STOCK INDEX OPTION

An option, either exchange-traded or over-the-counter, on a stock index.

STOCK OPTION

An option, either exchange-traded or over-the-counter, on an individual equity.

STRADDLE

The sale or purchase of a put option and a call option, with the same strike price, on the same underlying and with the same expiry. The strike is normally set at-the-money. The purchaser benefits, in return for paying two premiums, if the underlying moves enough either way. It is a way of taking advantage of an expected upturn in volatility. Sellers of straddles assume unlimited risk but benefit if the underlying does not move. Straddles are primarily trading instruments. See also option combination strategies

STRANGLE

1.As with a straddle, the sale or purchase of a put option and a call option on the same instrument, with the same expiry, but at strike prices that are out-of-the-money. The strangle costs less than the straddle because both options are out-of-the-money, but profits are only generated if the underlying moves dramatically, and the break-even is worse than for a straddle. Sellers of strangles make money in the range between the two strike prices, but lose if the price moves outside the break-even range (the strike prices plus the premium received). 2.The term strangle is also used, by currency option traders, to denote the average difference in implied volatility between out-of-the-money call and put options with a 25% delta and the implied volatility of at-the-money forward options. See also option combination strategies

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STRAP

A strategy that involves purchasing one put option and two call options, all with the exact same strike price, underlyings and maturity date.

STRATEGIC ASSET ALLOCATION

The distribution of investment funds in response to long-term, fundamental expectations for markets.

STRESS-TESTING

To perform a stress test on a derivatives position is to stimulate an extreme market event and examine its behaviour under the ‘stress’ of that event.

STRIP

A strategy that involves the purchase of one call option and two put options, all with the same strike price on the same underlying and the same expiry date. The strikes are set at-the-money. Alternatively, a strip can refer to the process of removing coupons from a bond and selling the stripped bond (or zero coupon bond) and interest-paying coupons separately.

STRUCTURED PRODUCT

A structured product is an investment that bundles up a portfolio of securities and other derivatives to create a single product. For example, a structured note can be a five-year bond that has an embedded equity or currency option in order to enhance its return. A structured product appeals to the investor who has a view on the market and a good idea of what his risk/reward appetite is.

STRUCTURED YIELD INVESTMENTS

Any security (normally a structured note) whose yield is conditional on certain trigger conditions being met. Such a security is normally constructed by embedding path-dependent options (such as binary options) in a vanilla debt issue. The investor’s return on the note will then vary according to the payout of the options.

SUBSTITUTION OPTION

A bilateral financial contract in which one party buys the right to substitute a specified asset or one of a specified group of assets for another asset at a point in time or contingent upon a credit event.

SWAP

See accreting, credit default swap, delayed reset swap, digital swap, dual currency swap, equity (index) swap, forward swap, high-coupon swap, index amortising swap, interest rate swap, mortgage swap, municipal swap, participating swap, periodic resetting swap, power swap, puttable swap, reverse index 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

SWAPTION

An option to enter an interest rate swap. A payer swaption gives the purchaser the right to pay fixed, a receiver swaption gives the purchaser the right to receive fixed (pay floating). Apart from those in the sterling market, many swaptions are capital-market driven. Good-quality borrowers are able to issue puttable or callable bonds and use the swaptions market to reduce their financing costs. In the case of callable bonds, the issuer effectively buys an option from the investor in return for a slightly higher coupon, so that it may benefit if rates decline. Because many of these embedded options have traditionally been underpriced, good-quality borrowers have been able to monetise this anomaly by selling an equivalent swaption (a receiver swaption) to a bank at market rates. The profit from this arbitrage lowers funding costs. If the swaption is exercised against the issuer, it calls the bonds (although the issuer would almost certainly have called the issue given the reduction in rates). In the case of puttable bonds, the borrower sells a swaption to the swaption market. The premium gained lowers the funding cost at the expense of leaving the borrower unsure of the maturity of the debt.

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SYNTHETIC ASSET

A synthetic asset is a combination of long and short positions in financial instruments, which has the same risk/reward profile as another instrument. For example, it is possible to replicate the payout and exposure of a short futures position by going short European-style call options and long European puts with identical strikes and expiries. Synthetic index options can be generated either through positions in the underlying and futures contracts, or with a basket of vanilla options. See also replication, static replication

SYNTHETIC COLLATERALISED DEBT

OBLIGATION

A synthetic collateralised debt obligation (CDO) uses credit derivatives to transfer credit risk in a portfolio. This is in contrast to a traditional CDO, which is typically structured as a securitisation with ownership of the assets transferred to a separate special purpose vehicle (SPV). The assets are funded with the proceeds of debt and equity issued by the vehicle. In a synthetic CDO, an institution transfers the total return or default risk of a reference portfolio via a credit default swap, a total return swap, or a credit-linked note. The SPV then issues securities with repayment contingent upon the loss on the portfolio. Proceeds are either held by the vehicle and invested in highly rated, liquid collateral, or passed-on to the institution as an investment in a credit-linked note. Balance sheet synthetic CDOs are typically used by banks to manage risk capital and are easier to execute than traditional CDOs. Arbitrage synthetic CDOs are often used by insurance companies 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 FORWARD

See synthetic asset

SYNTHETIC OPTION

See synthetic asset, replication

SYNTHETIC SECURITISATION

A first-loss basket swap structure that references a portfolio of bonds, loans or other financial instruments held on a firm’s balance sheet. The technique replicates the credit risk transfer benefits of a traditional cash securitisation while retaining the assets on balance sheet. Advantages over cash securitisation include reduced cost, ease of execution and retention of on-balance sheet funding advantage.

SYSTEMIC RISK

The risk that the financial system as a whole may not withstand the effects of a market crisis. Concern on the part of banking regulators has been caused by the concentration of derivative risk among a relatively small number of market participants, with the concomitant risk that the failure of a major dealer could have serious knock-on effects for many other market participants.

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TABLE TOP

Similar to a ratio spread, except that the purchase of an option is financed by sales of the same option at two different strike prices.

TACTICAL ASSET ALLOCATION

The distribution of investment funds in response to short-term expectations of market opportunity or threat.

THETA

This measures the effect on an option’s price of a one-day decrease in the time to expiration. The more the market and strike prices diverge, the less effect theta has on a vanilla option’s price. Theta is also non-linear for vanilla options, meaning that its value decreases faster as the option is closer to maturity. Positive gamma is generally associated with negative theta and vice versa.

S/T


TIME DECAY

See theta

TIME VALUE

The value of an option, other than its intrinsic value. The time value therefore includes cost of carry and the probability that the option will be exercised (which in turn depends on its volatility).

TOTAL RETURN SWAP

A bilateral financial contract in which one party (the total return payer) makes floating payments to the other party (the total return receiver) equal to the total return on a specified asset or index (including interest or dividend payments and net price appreciation) in exchange for amounts that generally equal the total return payer’s cost of holding the specified asset on its balance sheet. Price appreciation or depreciation may be calculated and exchanged at maturity or on an interim basis. A total (rate of ) return swap is a form of credit derivative, but is distinct from a credit default swap in that floating payments are based on the total economic performance of a specified asset and are not contingent upon the occurrence of a credit event.

TOTAL RETURN OPTION

A total return option is a put option on debt. An investor that has a risky corporate bond and is worried about default can buy a total return option that allows him to sell the bond at par if the corporation defaults.

TRACKING ERROR

Refers to the difference between the performance of a portfolio of stocks and a broad-based index with which they are being compared.

TRANCHE PRODUCT

A tranche product is one that is open for subscription for only a limited period, as opposed to open-ended products, which accept investments for an unlimited period. Most structured products are

tranche products, and the offer period is usually 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 for foreign operations.

TREASURY LOCK

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

TRIGGER

Many path-dependent options have payouts that depend on the underlying asset or index or coupons paid/payable reaching a specified level before the expiry date. This level is the trigger. Some options have more than one trigger level, in which case the payouts are conditional or increase with the number of triggers activated or the order in which they are activated. See barrier option, Parisian barrier option

TRIGGER CONDITION

Path-dependent derivatives such as barrier options and binary options have payouts which depend in some way on a market variable satisfying a specific condition during the derivative’s life. If this ‘trigger condition’ is met, the derivative may pay out immediately (early exercise) or at some other specified time (such as expiry). Alternatively, the option may only become effective (be knocked-in) or be de-activated (knocked out) when the trigger condition is met. The most common condition is that the spot rate or price of the underlying must breach a specified level, meaning that it must trade through the barrier, either from above or below. Many other trigger conditions are possible, however. Some examples include: ¦¦the spot must breach the trigger, and remain above/below it for a specified time; ¦¦the spot trades at the trigger level at a specified time (eg, expiry) or at any time during the option’s life;

T


¦¦the spot trades within or breaks out of a range (for example, range binaries); ¦¦there is more than one trigger level, with the payout conditional upon or increasing with the number of triggers activated and possibly the order in which they are activated (for example, a mini-premium option); ¦¦some combination of these. See also barrier option, Parisian barrier option, range binary

TRIGGER FORWARD

The trigger forward is primarily designed for trading purposes, although it can also be used as an alternative hedge. It is usually a zero-cost structure, whereby the purchaser enters into an outright forward transaction at a rate significantly more attractive than the prevailing market rate, but where the whole structure will be knocked out if a predetermined trigger level is reached at any time before the expiry date.

TRINOMIAL TREE

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

TURBO

A type of path-dependent option, usually embedded in warrants. A barrier is set at the same level as the strike price, and if the underlying ever touches the barrier at any point during the life of the turbo option, this will immediately cause the warrant to expire worthless. If the underlying never reaches the strike during the option’s life, the payout will be similar to a vanilla warrant.

TWO-FACTOR MODEL

Any model or description of a system that assumes two sources of uncertainty or variables; for example, an asset price and its volatility (a stochastic volatility model),

or interest rate levels and curve steepness (a stochastic interest rate model). Two-factor models model interest rate curve movements more realistically than one-factor models.

TWO-NAME EXPOSURE

Credit exposure that the protection buyer has to the protection seller, which is contingent on the performance of the reference credit. If the protection seller defaults, the buyer must find alternative protection and will be exposed to changes in replacement cost due to changes in credit spreads since the inception of the original swap. More seriously, if the protection seller defaults and the reference entity defaults, the buyer is unlikely to recover the full default payment due, although the final recovery rate on the position will benefit from any positive recovery rate on obligations of both the reference entity and the protection seller.

U

UNDERLYING

The underlying of a structured product or option can be any asset class (equity index, stock basket, debt instrument, interest rate, commodity or a combination of these) that is used to construct the product and whose performance is a key determinant of the payout. In some products, the underlying may be a basket of 20 stocks, but the redemption basket that is used to calculate the maturity payout may comprise only 10 of those stocks.

UNDERWATER

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

UP-AND-IN

A type of barrier option that pays off only when the underlying index reaches the upper barrier during the life of the option.

UP-AND-OUT

A type of barrier option that knocks out when the underlying reaches the strike.

T/U


V

VALUE-AT-RISK

Formally, the probabilistic bound of market losses over a given period of time (known as the holding period) expressed in terms of a specified degree of certainty (the confidence interval). Put more simply, the value-at-risk (VaR) is the worst-case loss expected over the holding period within the probability set out by the confidence interval. Larger losses are possible, but with a low probability. For instance, a portfolio whose VaR is $20 million over a one-day holding period, with a 95% confidence interval, would have only a 5% chance of suffering an overnight loss greater than $20 million. Calculation of VaR entails modelling the possible market moves over the holding period, incorporating correlations among market factors, calculating the impact of such potential market moves on portfolio positions, and combining the results to examine risk at different levels of aggregation. The three main approaches to this analysis are historical simulation, the analytical approach using a correlation matrix or empirical (Monte Carlo) simulation. Major trading houses expend considerable energies on their VaR methodologies and have lobbied regulators to recognise their efforts, with some success.

VANILLA OPTION

Also known as a plain vanilla option. A vanilla option is a standard call or put option in its most basic form.

VANNA

The vega of an option is not constant. Vega changes as spot changes and as volatility changes. The vanna of an option measures the change in vega for a change in the underlying spot. As spot moves deeper out-of-the-money for a vanilla option the vega is lower. If spot and volatility movements are positively correlated the holder of an option with positive vanna will be expected

to profit from this correlation. See also vega

VARIABLE NOTIONAL OPTION/SWAP

An option or swap where the notional value is linked to the underlying asset price or rate. Usually changes in the notional will be directly proportional to changes in the underlying price; ie, they both decrease or increase together. Such derivatives have two main uses. In an equity swap, the fixed-rate receiver can opt 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 amount for the swap. An example using an option is the case of a firm that sells more exports as exchange rates decline and its products therefore become cheaper abroad. Since it now has greater foreign currency revenue to hedge, it would purchase a variable notional currency option for this purpose.

VARIANCE GAMMA MODEL

A jump model that better captures the characteristics of the volatility smile for shorter-dated options than stochastic volatility models.

VARIANCE SWAP

The cash payout of a variance swap is equal to notional multiplied by the difference between the realised variance of the underlying index over the life of the swap and the strike variance.

VASICEK MODEL

An interest rate model that incorporates mean reversion and a constant volatility for the short interest rate. It is a one-factor model from which discount bond prices and options on those bonds can be deduced. All have closed-form solutions.

VEGA

Measures the change in an option’s price caused by changes in volatility. Vega is at its highest when an option is at-the-money. It decreases the more the market and strike prices diverge. Options closer to expiration have a lower vega than those with more time to run. Positions with positive vega will

V


generally have positive gamma. To be long vega (to have a positive vega) is achieved by purchasing either put or call options. Positions that are long vega benefit from increases in implied volatility but also from actual volatility if the option is being delta hedged. They will also lose from reductions in volatility. Spread options can be an exception: a reduction in the volatility of one of the assets may actually increase the price of the option because the correlation between the two assets decreases. Vega is sometimes known as kappa or tau. See also gamma, vanna, vomma

VERTICAL SPREAD

Any option strategy that relies on the difference in premium between two options on the same underlying with the same maturity, but different strike prices. Thus put spreads and call spreads would both be vertical spreads. Volatility A measure of the variability (but not the direction) of the price of the underlying instrument. It is defined as the annualised standard deviation of the natural log of the ratio of two successive prices. Historical volatility is a measure of the standard deviation of the underlying instrument over a past period. Implied volatility is the volatility implied in the price of an option. All things being equal, higher volatility will lead to higher vanilla option prices. In traditional Black-Scholes models, volatility is assumed to be constant over the life of an option. Since traders mainly trade volatility, this is clearly unrealistic. New techniques have been developed to cope with volatility’s variability. The best known are stochastic volatility, Arch and Garch.

VOLATILITY SKEW

The difference in implied volatility between out-of-the-money puts and calls. In most equity option markets out-of-the money calls have lower implied volatility than out-of-the-money puts. This is mostly ascribed to the greater supply of volatility above, rather than below, the money since fund managers are happy to write calls and not so happy to write puts. Volatility skews can be very pronounced in the currency markets although whether puts or calls are favoured depends on market sentiment

and demand and supply. See also implied volatility, risk reversal

VOLATILITY SMILE

A graph of the implied volatility of an option versus its strike (for a given tenor) typically describes a smile-shaped curve – hence the term ‘volatility smile’. This can be attributed to the belief that the underlying distribution is leptokurtic, since this tends to increase the value of out-of-the-money options.

VOLATILITY SWAP

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

VOLATILITY TERM STRUCTURE

The term structure of volatility is the curve depicting the differing implied volatilities of options with differing maturities. Such a curve arises partly because implied volatility in short options changes much faster than for longer options. However, the volatility term structure also arises because of assumed mean reversion of volatility. The effect of changes in volatility on the option price is less the shorter the option. Most market-makers take advantage of differing volatilities to hedge their books or to trade perceived anomalies in volatility. Such strategies have to be weighted because of the differing vega effects. See also implied volatility

VOLATILITY TRADING

A strategy based on a view that future volatility in the underlying will be more or less than the implied volatility in the option price. Option market-makers are volatility traders. The most common way to buy/sell volatility is to buy/sell options, hedging the directional risk with the underlying. Volatility buyers make money if the underlying is more volatile than the implied volatility predicted. Sellers of volatility benefit if the opposite holds. Other methods of buying/selling volatility are to buy/sell combinations of options, the most usual being to buy/sell straddles or strangles. Other strategies take advantage of the difference between implied volatilities of differing maturity options, not between

V


implied and actual volatility. For example, if implied volatility in short-term options is high and in longer options low, a trader can sell short-term options and buy longer ones.

VOMMA

The vega of an option is not constant. Vega changes as spot changes and as volatility changes. The vomma of an option is defined as the change in vega for a change in volatility. Vomma measures the convexity of an option price with respect to volatility. Vega is to vomma (volatility gamma) as delta is to gamma for spot movements. Holders of options with a high vomma benefit from volatility of volatility. See also vega

W

WARRANT

An instrument giving the purchaser the right, but not the obligation, to purchase or sell a specified amount of an asset at a certain price over a specified period of time. Warrants differ from options only in that they are usually listed. Underlying assets include equity, debt, currencies and commodities. See also equity warrant

WASTING ASSET

A wasting asset is a derivative security that loses value due to time decay and which may expire worthless at maturity. Derivatives such as options, rights and warrants are considered to be wasting assets.

WEATHER DERIVATIVE

Typically swaps and vanilla options such as calls, puts, caps, floors and collars with payouts linked to temperature, precipitation, humidity or windspeed. Most instruments are linked to heating degree days or cooling degree days. These two indexes measure the deviation of the average of a day’s high and low temperature from a baseline reference temperature.

WEDDING CAKE DEPOSIT

A type of range deposit where there is an inner range and one or more outer ranges. The payout from the product is at its maximum when the underlying remains in the inner range, and this is reduced successively when the spot reaches each outer range. This product is suitable for investors who have a range-bound view, and want to take less risk.

WEEKLY RESET FORWARD

A weekly reset forward is a synthetic forward where a portion of the contract is locked in each week, provided that the spot rate that week meets a predetermined fixing criterion. Hence the purchaser can deal at a rate better than the forward outright, but only in an amount corresponding to the frequency with which the criterion has been met. If the criterion is met in none of the weeks during the life of the contract, then the contract is not activated at all; if it is met every week, the overall rate is favourable compared with the initial prevailing market rate. The weekly reset forward is used for those with cash-flows spread over time or to hedge balance sheets.

WINDOW BARRIER

A window barrier is a type of barrier option for which the barrier strike only applies for a specified period during the option’s life. If the spot breaches this level during the window period, then the option either knocks in or knocks out. If the option is not activated during the window period, the option will retain the features of a vanilla option and expire at maturity.

WORST-OF OPTION

An option whose payout is referenced to one or more of the worst performers in a basket of shares or indexes.

V/W


Y

YIELD

The interest rate that will make the present value of the cashflows from an investment equal to the price (or cost) of the investment. Also called the internal rate of return. The current yield relates the annual coupon yield to the market price by dividing the coupon by the price divided by 100 and ignores the time value of money or potential capital gains or losses. Simple yield to maturity takes into account the effect of the capital gain or loss on maturity of a bond in addition to the current yield.

YIELD ADJUSTMENT

A payment by one counterparty, usually at the outset of a swap or at a reset date, to compensate the other counterparty for entering into a swap on off-market terms.

YIELD CURVE

The yield curve is a graphical representation of the term structure of interest rates. It is usually depicted as the spot yields on bonds with different maturities but the same risk factors (such as creditworthiness of issuer), plotted against maturity. The usual features of a spot yield curve are higher long-term yields than short-term yields and a curve for default-free bonds that is lower at each point than the equivalent curve for riskier debt. It is possible to construct variants of the yield curve from this basic form. The par yield curve is found by calculating the coupons that would be necessary for bonds of each maturity to be priced at par; the forward yield curve is found by extrapolating the spot yield curve point-by-point, based on the implied forward interest rates.

YIELD CURVE AGREEMENT

See yield curve swap

YIELD CURVE OPTION

An option that allows investors to take a view on the shape of a yield curve without

taking a view on a bond market’s direction. It is normally structured as the yield of a longer maturity bond minus the yield of a shorter one. A call would therefore appreciate in value as a curve flattened. A put would decrease in value. Such options were developed in the US in 1991 in response to a steepening yield curve.

YIELD CURVE SWAP

A swap in which the two interest streams reflect different points on the swap yield curve. Yield curve swaps can be used to exploit a yield curve steepening or flattening view. For example, one side pays the two-year Constant Maturity Treasury (CMT) rate and the other the 10-year CMT rate.

Z

ZERO COST COLLAR

See zero cost option

ZERO COST OPTION

Any option strategy that involves financing an option purchase by the simultaneous sale of another option so that paid and received premiums exactly offset one another. See also collar, participating forward Zero coupon bond A 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 or both of the counterparties makes one payment at maturity. Usually it is the fixed-rate payments only that are deferred. The party not receiving payment until maturity incurs a greater credit risk than it would with an ordinary swap. The swap is advantageous for a company that will not receive payment for a project until it is completed or to hedge zero coupon liabilities, such as zero coupon bonds.

ZERO EXERCISE PRICE OPTION (ZEPO)

A low exercise price option whose strike price

is exactly zero.

Y/Z

Europe

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