Topic 12a

Primer on Derivative Instruments:Futures, Options, and Risk Management

Chapter 13 (Blackwell, Griffiths, and Winters) and other material

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Derivative Instruments

This section provides an overview of key derivative instruments

• Futures contracts

• Forwards contracts

• Option contracts

• Swap contracts

Uses

• Speculation

• Hedge a cash position

• Traders and Arbitraging

• Alter the cash flow characteristics of a financial instrument

• Create a synthetic financial instrument

Derivatives derive their value from other instrument

• Futures, forwards and options derive their value from the behavior of the cash market

• Interest rate swaps derive their value through the behavior of spot interest rates

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Futures and Forward Contracts

Legal agreement • to buy or sell an item• in which the buyer (or seller) agrees to • take deliver (or to make delivery) of the item• at a specified time and• at a specified price

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Futures Versus Forward Contracts

Futures ContractsStandardized as to

• Delivery date• Quality

Traded on an organized exchangeExchange guarantees counterparty

performance (in effect, the exchange is the counterparty)

Typically not intended for settlement by delivery; position typically closed prior to expiration

Marked to market each dayMargin RequirementDaily limit on price movement

Forward ContractsNonstandardized

• Each is negotiated as to quantity and delivery date

Often a poor secondary marketOTC instrumentSettlement by deliveryNot marked to marketNo margin requirement

• Hence, there is no interim cash flow

Obligation of the issuer• Hence, there is performance risk

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Futures Versus Forward ContractsContinued

Futures Contract

•Typically settled before maturity, I.e, they are not settled by delivery

•Futures contract is best used when party does not desire to make (or take) delivery, and flexibility on date or size is not critcial

Forward Contract

•Forward contracts are typically held until maturity

•Settled by delivery

•Forward contract is used when need flexibility as to date and size, and when party seeks to take delivery or make delivery of the contract item

•The foreign exchange market is the largest user of financial forward contracts

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Liquidating Futures and Forward Contracts

Futures contracts

• Very liquid instrument

• It can be liquidated in two ways

• At maturity by fulfilling the terms

• Before maturity by taking an offsetting position

Forward contracts

• More difficult to offset due to its negotiated maturity

• Can be liquidated only through purchase of offsetting contract; but holder may not be able to obtain the offset from the issuing institution

• Forward contracts are typically held until maturity

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Financial Futures

DomesticStock indexes

S&P 500S&P mid capDJIANikkie 225Nasdaq

Money market instrumentsFederal fundsTreasury billsEurodollarsLIBOREurocurrencies - Euroyen

BondsTreasury notesTreasury bondsMuni-bonds

Foreign currencies

Foreign

Money market

Euroyen

Euromark

Short sterling

Euroswiss

Bonds

Long sterling (guilts)

German gov’t bonds

Italian gov’t bonds

Canadian gov’t bonds

French gov’t bonds

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Settlement of Financial Futures at Maturity

The settlement depends on the instrument:• Treasury bills futures: delivery• Eurodollars futures: cash• Treasury bonds futures: delivery• S&P index futures: cash

A contract is rarely held until settlement• Typically, the contract is “closed out” through a

opposite contract• As a result, contracts that settle by delivery typically do

not deliver the instrument or the commodity

Financial FuturesMargin Requirement and Leverage

Differs from a stock margin

• Margin deposit is required as good faith that buyer or seller will perform

Position is marked to market each day

• If price falls deposit is reduced; if price rises, deposit is increased

• If margin deposit falls beneath pre-set minimum, a margin call is made

If a call is not met with cash or securities, the position is closed by issuing an offsetting contract.

Cash outlay is equal to the margin deposit

• This is the cash investment against which gains and losses are calculated

As a result, investor can us futures to buy or sell a multiple of the underlying cash instrument for a given cash outlay

This increases the potential gain (or loss) return on invested funds in a futures compared with a cash instrument

Implications: Futures are risky

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Long Versus Short Position

Long Position: Buy a futures contract:

Agree to take delivery of the item at the settlement date for the futures price

Short Position: Sell a futures contract

Agree to delivery the item at the settlement date for the futures price

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Pricing a Futures ContractEurodollar (Money Market) Futures

Settlement Pricing:

• Money market futures are priced on an index basis

• Settlement price in index terms• QF = 100 - ID

• If quote is 94.75, the implied rate is 5.25%

• Dollar settlement price depends on the maturity of the instrument involved

• The Eurodollars contract assumes a 90 day instrument

• For a 1,000,000 contract, dollar settlement price is• {[100 - 5.25 x (90/360)]/100}x 1,000,000 = 986,875

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Pricing a Futures ContractBond Futures Contract

Bond contracts are for a hypothetical bond maturing in exactly 30 years with a $100,000 face value and a coupon of 6%

Suppose that the December 2014 30-year bond futures contract is

106:8 (Remember: this is expressed as % of face value in 32nds)

Converting 32nds to decimal:

106.25

The notional value of one contract is

1.0625*$100,000=106250

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Pricing a Futures ContractS&P500 Stock Index Futures Contract

The price of the S&P futures contract is

Suppose the index for the December 2014 futures contract is 969.30

The price of one contract would be:

$ 2 5 0 index

$ 2 5 0 . $ 2 4 2 , 9 6 9 3 0 3 2 5

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Using Money Market FuturesGain (Loss) on a Long Position

Suppose that 20 December 2014 Eurodollar contracts are position bought (sold) and the settlement price is 93.60

• Dollar or notional price is• {[100 - 6.4 x (90/360)]/100}

x 20,000,000• 19,680,000

Suppose that in 1 day the price is 94.25, what is the gain of loss?

• Dollar or notional price is• {[100 - 5.75 x (90/360)]/100}

x 20,000,000• 19,712,500

Since this is a long position, the holder benefits from a rise in price and the profit is

• 19,712,500 - 19,680,000

• 32,500

If this were a short position (the sale of 20 contracts) there would have been a loss of the same amount

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Using Treasury Bond Futures

Suppose that the December 2014, 30-year bond futures contract is106:8 (Remember: this is expressed as % of face value in

32nds)

The notional value of one contract is1.0625*$100,000=106250

Suppose that the next day, the contract price is106:9

The notional value of one contract would be1.0628125*100,000=106281.25

Margin account for 1 long contract would have increased by$31.25

Margin account for 1 short contract would have decreased by$31.25

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Background Use OnlyUsing Barclay Broad Aggregate Index

Futures

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Contract size = 100 x Futures Index ValueDecember Index Value 1670.01 contractnotional value = 1670.0 x 100 = $167,000.00Notional value of 15 contract $2,505,000.00Settlement Index Value tomorrow 1671.8Notional Vlaue of 15 contract $2,507,700.00Gain (loss) for long $2,700.00Gain (loss for short -$2,700.00

Background Use OnlyUsing FX Futures

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value in dollarsbuy 1 contract 125,000.00 € $/euro at 1.3333 $166,662.50

125,000.00 € $/euro at 1.3322 $166,525.00

long euros and the dollar rose -$137.50

value in dollarssell 1 contract 125,000.00 € $/euro at 1.3333 $166,662.50

125,000.00 € $/euro at 1.3322 $166,525.00

short euros and the dollar rose $137.50

Hedging Uses of Financial Futures

Textbook UsesReducing systemic risk in stock

portfoliosTo change the maturity of an assetLocking in a borrowing rateGuaranteeing the cost of fundsFunding fixed rate loansLock-in return

Covered foreign investmentsHedge unrealized profit against price drop

Hedge a balance sheet (duration based hedging)

Create synthetic instruments

Basic uses To hedge income

Interest income: protect against a fall

Interest expense: protect against a rise

To hedge value

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Illustrating a Long and Short Hedges

Long hedge:

• Long position (buy future contracts) on belief that interest rates will fall (price rise)

and

• The hedger would be harmed by

a fall in rates (rise in price)

Short hedge:

• Short position (sell a futures contract) on belief that interest rates will rise (price will fall)

and

• Hedger would be harmed by a rise in rates (fall in price)

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Risk Action

(Expense hedge) A bank expects to roll over a sizable volume of retail CDs in November; rates may rise, costing the bank more for those deposits

(Income hedge) A bank is expecting a sizable loan in November; rates may fall reducing the rate received on the loan

Short hedge; sell Eurodollar futures contracts; gain from the closeout (price falls) would be used to reduce the amount of deposits that the bank must retain

Long hedge; buy Treasury note security closely matching the maturity of the loan; gain from the closeout (price rises) would be used to reduce the amount of funds the bank would need to borrow to make the loan

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Risk Action

(Value hedge) A managers of an index portfolio (S&P500) thinks the market is over valued

(Value hedge) A pension fund manager fells that the S&P is under valued; he will receive a inflow of funds from the manager in at the end of September

Short hedge; sell S&P500 future contracts (the action effectively sells a portion of the portfolio today at a given price for a future deliver

Long hedge; buy S&P 500 future contracts (the action effectively buys the S&P500 today for a given price with a given delivery date

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Risk Action

A bank expects to roll over a sizable volume of retail CDs in November; rates may fall

A bank is expecting a sizable loan in November; rates may rise

Nothing, this outcome benefits the bank

Nothing; this outcome benefits the bank, though it may want to hedge borrowing costs

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Hedging Value

Hedges can be used to hedge against adverse effects on income or value

Value hedges come in two general forms; these alter the market-risk characteristics of a stock portfolio or the duration of a portfolio through futures

• Beta hedges: This hedges the value of a single stock or a portfolio where beta serves as the measure of market risk

• Single stock

• Portfolio hedge

• Duration-based hedges

• Hedging a portfolio

• Hedging net worth

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Beta-Based Hedge RatioSingle Stock

Situation:

• You have accumulated 3,500,000 shares of Cosmic Sciences

• The stock is restricted and you cannot sell it until June 10, 2015

• It is presently valued at $87.5 per share and you are concerned with a the market’s current level

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Cosmic Widgets Stock

The basic questions

• Since you are concerned with decline in the market (market or systemic) risk, a possible hedge instrument is the S&P500 stock index

• The contract should be the June 2015 contract

• Its index price is 1237.5

• Since the concern is a price drop, you would want a short hedge

• The number of contracts depend upon the stock beta

Suppose that its beta is 3.5 (very risky relative to the market)

The hedge ratio becomes:

Nf = x (value of the stock / contract price)

= 3.5 x (87.5 x 3,500,000)/( 250*1237.5)

= 3.5 x 303464.6250,000/309375

= 3464.6464 contracts

rounded to

= 3465 contracts

Question : can you hedge its idiosyncratic risk through futures? No

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Hedging Systemic RiskAn Example Using A Stock Portfolio

Futures can be used to transfer systemic risk to another partySuppose you have a portfolio $15,000,000 that mirrors the S&P

500• Next, suppose that you wish to protect against a fall in the

value of the portfolio through December 31, 2014• A short hedge would provide this protection

Which contract: March 2015Index value of March 2015 1000.20How many contracts: Notional value / contract price

15,000,000 / (250x1000.20) 60 contracts

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Hedging Systemic Risk An Example Using A Stock Portfolio - Continued

How does the hedge work

• If the price of the futures contract falls in tandem with the spot or cash price, the gain from the short hedge will offset the loss in the value of the portfolio

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Hedging Systemic RiskAn Example Using a Bond Portfolio

• The weighted modified duration of a portfolio is

• Dm

• The change in the value of the portfolio is

• P = - DmyP

• The modified duration of the futures contract is

• DmF

• The change in the value of the futures position is

• F = - DmFy PF

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Hedging Systemic RiskAn Example Using a Bond Portfolio - Continued

• Futures will be used to protected against the possibility of a price decline in the value of the portfolio for a given increase in rates

• The question is then, given the modified duration of the hedged instrument (the portfolio) and of the hedge instrument (the Treasury bond futures contract), how many contracts must used

• To answer this, keep in mind that the gain in the value of the futures contract will be used to offset the loss in value in the portfolio

• This is achieved when:

P - nF = 0

• In other words, the gain from a short position in Treasury bond futures would offset the loss in value of the portfolio

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Hedging Systemic RiskAn Example Using a Bond Portfolio - Continued

• The number of futures contracts to be sold should be chosen so that any change in the value of the value of the portfolio (the underlying instruments) is offset by a change in the value of the futures contract

• This occurs when P = - n F

• n = - {P / F}

• Since DP is negative (a loss in value) and DF is positive, the two negatives lead to a positive

• Or• n = {P / F}

• Upon substitution and rearranging terms

• n = - {DmPy / DmFPFy}

• Since the modified duration is duration divided by 1+y, this becomes

• n = {DP / DFPF}• The portfolio hedge would be

established only when there was an expectation of a fall in the price of the portfolio.

Background Use; see EXCEL mini-casesPortfolio Immunization

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A: The manger expects interest rates to fallActual Portfolio Duration 4.3525Duration of 30-year futures contact 11.79121061Portfolio $255,755,225.00Futures index 124.5617146Notional value of 1 contract 124561.7146Hedge ratio -$757.91B. Number of contracts rounded -758

Consider a portfolio with a modified durtaion of 4.3525. Next suppose that the manager wants to fully immunize the portfolio against changes in interest rates. (A) Under what cirrcumstance would the manager make this decision? (B) How many contracts would be needed? (C) Is is a long or a short position?

C. A short position, since the manager wants to reduce the duration to zero

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Hedging Systemic RiskAn Example Using a Bond Portfolio - Continued

• This hedge must be continuously recalibrated as interest rates change since duration depends upon interest rates

• Also, if the portfolio is not precisely the same instrument as the hedge, a hedge ratio must be found to link the underlying portfolio and the hedge instrument

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Changing Duration Using Treasury Bond Futures

• Suppose that • The target duration of an asset portfolio is D

• and the actual duration of the portfolio is DF

• The target duration can be achieved by

• n = number of futures contracts• F = price of futures contract

pFp P

nFxDDD

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Changing Duration Using Treasury Bond FuturesContinued

Solving for n yields

If n is positive:• It represents a long position• If Da is less than D this will length the duration of the

portfolioIf n is negative:

• It represents a short position• If D is less than Da this will shorten the duration of the

portfolio

F

Px

D

DDn p

F

p

Background Use Only: See EXCEL Mini-case Using Long-Term Treasury Futures to

Change a Portfolio’s Duration

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A: The manger expects interest rates to fallActual Portfolio Duration 4.3525Target Duration 4.4255Duration of 30-year futures contact 11.79121061Portfolio $255,755,225.00Futures index 124.5617146Notional value of 1 contract 124561.7146Hedge ratio 12.71B. Number of contracts rounded 13

Consider a portfolio with a modified durtaion of 4.3525. Next suppose that the manager wants to length the duration. (A) Under what cirrcumstance would the manager make this decision? (B) How many contracts would be needed? (C) Is is a long or a short position?

C. A long position, since the manager wants to lengthen the duration

Background Use OnlyHedging with FX Futures

Suppose that a U.S. Firm will receive a payment of 50,000,000E on December 12, 2014

• Today’s $/E rate is 1.4704

• You are concerned that the dollar will depreciate, would you hedge? No because the dollar value of the euros will rise

If you expect the dollar to appreciate, you would want to own the euros now; a short hedge would lock in the dollar value of the payment.

Steps are on the next slide

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Background Use OnlyHedging with FX Futures

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Hedge ration = 50,000,000/125,000 = 400

Number of Contracts

Notional Contact Value

June Futures

RateContract

Rate as ofNotional

Contact in dollar400 50,000,000.00 € 1.4605 10/3/2012 $73,025,000.00400 50,000,000.00 € 1.342 12/12/2012 $67,100,000.00

gain (loss) onshort position positions $5,925,000.00Cash FX

rateCash Rate as

of Dollar Value of

the Payment1.4704 10/3/2012 $73,520,000.001.3425 12/12/2012 $67,125,000.00

-$6,395,000.00

Payment of 50,000,000E will be made by a Europen firm to a U.S. firm firm on 12/12/14. If dollar rises, the dollar value of the payment would be worth less. A short hedge can protect the dollar value of the payment

Gain on the short position offsets the decline in the dollar value of the payment. But, hedge was incomplete due to basis risk; spread between cash and futures changed betweem now and December

Background Use OnlyHedging with FX Futures

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Hedge ration = 145,525,000/125,000 = 1164.2

Number of Contracts

Notional Contact Value

June Futures

RateContract

Rate as ofNotional

Contact in dollar1164.2 145,525,000.00 € 1.3338 10/3/2012 $194,101,245.001164.2 145,525,000.00 € 1.3345 12/12/2012 $194,203,112.50

gain (loss) on hedge positions $101,867.50Cash FX rateCash Rate as of

1.3336 4/3/2012 -$194,072,288.031.3342999 6/12/2012 -$194,174,140.33

-$101,852.30

Payment of 145,525,000,000E will be made by a U.S. firm to a European firm on 12/12/14. If dollar falls, the dollar cost of the payment would rise. Long Hedge can protect against this risk

Gain on the long position offset the higher dollar cost to to the dollar fall. But, hedge was incomplete due to basis risk; spread between the cash and the futures changed between now and December

Cross Hedge

Seek to hedge one instrument for which a contract is not offered. So, hedger must buy a contract with which the hedged instrument is closely related

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Hedge Decisions

• Type of hedge: long or short hedge

• Choice of hedge instrument

• Maturity or expiration date of the contract

• Number of contracts

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Hedge Decision

Type of hedge

Long hedge or short hedge

Read the situation very carefully and determine against what risk you seek protection

Earlier slides that summarize long and short hedges lay out the risks that each of the two hedges seek to protect you against

Choice of hedge instrument

Choose the hedge instrument whose price change is most closely related to the instrument to be hedged

• A bank would not hedge the rate on a 2-year loan with Eurodollars; it would use the 2-year Treasury note

• A tech stock portfolio would not use the S&P stock index futures; it would likely use the NASDAQ100 futures contract

In most cases, there is not a match between the type of instrument to be hedged and the available hedge instruments

• A cross hedge is used which heightens the risk that the hedge may be incomplete

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Hedging Decision

Maturity of the hedge contract

• Maturity of the contract should be beyond the point at which the hedge would be close out

• E.g., if the hedge is to protect income of value through 12/31 of the year, you would use the March contract

• If contracts are not available for that length of time, the hedge would do a rollover hedge, I.e., after the first contract matures, repeat the hedge

Number of contracts

• This is known as the hedge ratio

Simple hedge ratio =

dollar amount to be hedged / notional value of one contract for the hedge instrument

Beta hedge ratio

Duration-based hedge ration

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Incomplete HedgeAn incomplete hedge can result from a variety of sources

Incomplete hedge stems from a failure

• to identify the proper instrument, or

• to estimate the proper relationship between the hedge instrument and the instrument to be hedged

Sources:

• Basis Risk:

• Relationship between the spot price and the futures contract price may change

• Cost of carry could change

• Relationship between the hedged instrument and the hedging instrument changes

• This is common in a cross hedge

• Related contract

• Hedge funding cost of loan but loan is prepaid due to drop in rates

• Bank looses on the short-sale of futures contract and receives no offset from the commercial loan because it is paid off.

• Manipulation Risk

• Short squeeze where speculators make it difficult for shorts to liquidate contracts before maturity

• Margin Risk

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Options

Right to buy (or sell) a commodity or asset at a set price up to a set date.

The option holder is NOT required to buy or sell. The option is exercised at the holders discretion

Predetermined price:

strike price

or

exercise price

Call option: right to buy a security at a specified price by a specified date

Put option: right to sell a security at a specified price by a specified date

Short call option, the investor is the writer of the call option and the buyer holds the call option

Short put option, the investor is the writer of the put option and the buyer holds the put option

Option buyer pays the option writer a fee for the option

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Call Option(Rule for Exercise)

Suppose the strike price is: 100

and the fee is: 3

if mkt price < 100 do not exercise

if mkt price 100 do not exercise

if mkt price 100 to 103 exercise to minimize loss

if mkt price = 103 exercise to break-even

if mkt price > 103 exercise for profit

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Put Option(Rule for Exercise)

Suppose the strike price is: 100

and suppose the fee is: 3

if mkt price > 100 do not exercise

if mkt price = 100 do not exercise

if mkt price 100 to 97 exercise to minimize loss

if mkt price < 97 exercise for a profit

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Payoff of Long Call and Long Put

Long call payoff Long put payoff

0

Strike Price

Strike Price

PremiumPremium

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Payoff of Short Call and Short Put

Short call payoff Short put payoff

0Premium Premium

Strike price

Strike price

48

Synthetic Long Futures PositionLong Call and Short Put

Payoff for long call

Payoff for short put

Payoff for futures contract

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Caps, Floor and Collars

CAPS

Cap on a loan or a security:

Limits interest rate exposure of borrower to rise in rates

Process: functions the same as a series of call options in which the writer (the holder of the instrument with the cap) agrees to pay the buyer of the option whatever additional interest rate he must pay on his loan, if rate rise above an agreed upon rate.

FLOORS

Purpose: to limit the exposure of a floating rate lender to a fall in rates

A floor may be part of a loan agreement which sets a minimum rate that will be paid by the borrower

Process: floor functions as a series of put options in which the writer (the borrower) guarantees the interest that he/she must pay on a loan, if the rate on that loan goes below an agreed upon level

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Collars

A combination of a cap and a floor

This limits the floating rate payment on both the up side and the downside of an interest rate cycle

It splits the interest rate exposure between a borrower and lender.

If rates rise above the cap, the borrower is protected from rising rates. If rates fall beneath the floor, the lender is protected. Between the cap and the floor, it is a floating rate loan

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