OPTIONS, CAPS, FLOORS AND MORE COMPLEX SWAPS

Chapter 11

Bank ManagementBank Management, 5th edition.5th edition.Timothy W. Koch and S. Scott MacDonaldTimothy W. Koch and S. Scott MacDonaldCopyright © 2003 by South-Western, a division of Thomson Learning

The nature of options on financial futures

An option…an agreement between two parties in which one gives the other the right, but not the obligation, to buy or sell a specific asset at a set price for a specified period of time.

The buyer of an option …pays a premium for the opportunity to decide whether to effect the transaction (exercise the option) when it is beneficial.

The option seller (option writer) …receives the initial option premium and is obligated to effect the transaction if and when the buyer exercises the option.

Two types of options

1. Call option…the buyer of the call has the right to buy the underlying asset at a specific strike price for a set period of time. the seller of the call option is obligated to

deliver the underlying asset to the buyer when the buyer exercises the option.

2. Put option…the buyer has the right to sell the underlying asset at a specific strike price for a set period of time. the seller of a put option is obligated to buy

the underlying asset when the put option buyer exercises the option.

Options versus futures

In a futures contract, both parties are obligated to the transaction

An option contract gives the buyer (holder) the right, but not the obligation, to buy or sell an asset at some specified price: call option, the right to buy put option, the right to sell

Exercise or strike price…the price at which the transaction takes place

Expiration date…the last day in which the option can be used

Option valuation

Theoretical value of the option: Vo = Max( Va - E, 0)

where Va = market price of the assetE = Strike or exercise price.

Example: Option to buy a house at $100,000 If market value is $120,000: Vo= Max( 120,000 - 100,000, 0) = 20,000 If market value is 80,000, Vo = 0

Options, market prices and strike prices…as long as there is some time to expiration, it is possible for the market value of the option to be greater than its theoretical value.

Call OptionsOut of the Money

Market price < Strike priceAt the Money

Market price = Strike price In the Money

Market price > Strike price

Put OptionsOut of the Money

Market price > Strike priceAt the Money

Market price = Strike price In the Money

Market price < Strike price

Option value: time and volatility

The longer the period of time to expiration, the greater the value of the option: more time in which the option may have value the further away is the exercise price, the

further away you must pay the price for the asset

The greater the possibility of extreme outcomes, the greater the value of the option volatility

Options on 90-day Eurodollar futures, April 2, 2002

Each option's price, the premium, reflects the consensus view of the value of the position.

Intrinsic value equals the dollar value of the difference between the current market price of the underlying Eurodollar future and the strike price or zero, whichever is greater.

StrikePrice June Sept. June Sept.

9700 0.53 0.25 0.02 0.419725 0.30 0.14 0.08 0.569750 0.18 0.09 0.19 0.739775 0.09 0.05 0.28 0.939800 0.02 0.01 0.49 1.17

Calls PutsOption Premiums*

Monday volume: 31,051 calls; 40,271 puts

Open interest: Monday, 4,259,529 calls; 3,413,424 puts

90-Day Eurodollar Futures Prices (Rates), April 2, 2002

June 2002: 97.52 (2.48%)

September 2002: 96.83 (3.17%)

The time value of an option equals the difference between the option price and the intrinsic value.

Consider the time values of the June 2002 call from 97.25 to 98.00 strike prices, the time values are $75, $400, $225, and $50, respectively, or 3, 16, 9, and 2 basis points.

Option premium…equals the intrinsic value of the option plus the time value: premium = intrinsic value + time value

The intrinsic value and premium for call options with the same expiration but different strike prices, decreases as the strike price increases. the higher is the strike price, the greater is the

price the call option buyer must pay for the underlying futures contract at exercise.

The time value of an option increases with the length of time until option expiration the market price has a longer time to reach a

profitable level and move favorably.

The intrinsic value of a put option is the greater of the strike price minus the underlying asset’s market price, and zero.

The time value of a put also equals the option premium minus the intrinsic value.

June put option at 97.50 was slightly out of the money --the June futures price, 97.52, was above the strike price. The 19 basis point premium represented time value.

Put options with the same expiration, premiums increase with higher strike prices Example: the buyer of a June put option at 98.00 has

the right to sell June 2002 Eurodollar futures at a price $1,200 (48 x $25) over the current price.

Option is in the money with an intrinsic value of $1,200 and a time value of $25 (one basis point).

Example: the September put options, the premiums rise as high as 117 basis points for a deep in the money option.

The time value is greatest for at the money put options, and time values increase the farther away an option’s expiration.

Buying or selling a futures position

Institutional traders buy and sell futures contracts to hedge positions in the cash market.

As the futures price increases, corresponding futures rates decrease.

Both buyers and sellers can lose an unlimited amount, given the historical range of futures price

movements and the short-term nature of the futures contracts, actual prices have not varied all the way to zero or 100.

Profit or loss in a futures position

Value of the Asset --------->

Profit

FuturesPrice97.52 97.52

A. Futures Positions

Loss

1. Buy June 2002 Eurodollar Futures at 97.52.

0

Profit

FuturesPrice

Loss

2. Sell June 2002 Eurodollar Futures at 97.52.

0

Trading call options

Buying a call option the buyer’s profit equals the eventual futures

price minus the strike price and the initial call premium

compared with a pure long futures position, the buyer of a call option on the same futures contract faces less risk of loss if futures prices fall yet realizes the same potential gains if prices increase

Selling a call option the seller’s profit is a maximum of the premium

less the eventual futures price minus the strike price

compared with a pure short futures position, the seller of a call option faces less potential gain if futures prices fall yet realizes the same potential losses if prices increase

Trading put options

Buying a put option a put option limits losses to the option premium,

while a pure futures sale exhibits greater loss potential

comparable to the direct short sale of a futures contract, the buyer of a put option faces less risk of loss if futures prices increase yet realizes the same potential gains if prices fall

Selling a put option a put option limits gains to the option premium,

while a pure futures sale exhibits greater gain potential

comparable to pure long futures position, the buyer of a put option faces less potential gain if futures prices increase yet realizes the same potential loss if prices fall

Profit or loss in an options position

Profit

FuturesPrice

FuturesPrice97.68

97.50 97.75

98.68

B. Call Options on Futures

Loss

1. Buy a June 2002 Eurodollar Futures CallOption at 97.50.

0

20.18

Profit

Loss

2. Sell a Sept. 2002 Eurodollar Futures CallOption at 97.75.

0

0.93

Profit

FuturesPrice

FuturesPrice

97.17

97.25

97.25

C. Put Options on Futures

Loss

1. Buy a June 2002 Eurodollar Futures PutOption at 97.25.

0

20.08

Profit

Loss

2. Sell a Sept. 2002 Eurodollar Futures PutOption at 97.25.

0

0.56

96.69

The use of options on futures by commercial banks

Commercial banks can use financial futures options for the same hedging purposes as they use financial futures.

Managers must first identify the bank’s relevant interest rate risk position.

Positions that profit from rising interest rates

Suppose that a bank would be adversely affected if the level of interest rates increases.

This might occur because the bank has a negative GAP or a positive duration gap, or simply anticipates issuing new CDs in the near term.

A bank has three alternatives that should reduce the overall risk associated with rising interest rates:

1. sell financial futures contracts directly2. sell call options on financial futures3. buy put options on financial futures

Profiting from falling interest rates

Banks that are asset sensitive in terms of earnings sensitivity or that commit to buying fixed-income securities in the future will be adversely affected if the level of interest rates declines. It can buy futures directly, buy call options on futures,

sell put options on futures, or enter a swap to pay a floating rate and receive a fixed rate.

Although the futures position offers unlimited gains and losses that are presumably offset by changes in value of the cash position, a purchased call option offers the same approximate gain but limits the loss to the initial call premium.

The sale of a put limits the gain and has unrestricted losses. The basic swap, in contrast, produces gains only when the actual floating rate falls below the fixed rate.

Several general conclusions apply to futures, options and swaps

1. Futures and basic swap positions produce unlimited gains or losses depending on which direction rates move and this value change occurs immediately with a rate move. Thus, a hedger is protected from adverse rate

changes but loses the potential gains if rates move favorably.

2. Buying a put or call option on futures limits the bank’s potential losses if rates move adversely. This type of position has been classified as a

form of insurance because the option buyer has to pay a premium for this protection.

Several general conclusions apply to futures, options and swaps (continued)

3. Determining the best alternative depends on how far management expects rates to change and how much risk of loss is acceptable.

4. Selling a call or put option limits the potential gain but produces unlimited losses if rates move adversely. Selling options is generally speculative and

not used for hedging.

Several general conclusions apply to futures, options and swaps (continued)

5. A final important distinction is the cash flow requirement of each type of position. The buyer of a call or put option must

immediately pay the premium. However, there are no margin requirements for

the long position. The seller of a call or put option immediately

receives the premium, but must post initial margin and is subject to margin calls because the loss possibilities are unlimited.

All futures positions require margin and swap positions require collateral.

Profit and loss potential on futures, options on futures positions, and basic interest rate swaps

Futures versus options positions… important distinction is the cash flow requirement of each type of position

The buyer of a call or put option must immediately pay the premium.

There are no margin requirements for the long positions.

The seller of a call or put option immediately receives the premium, but must post initial margin and is subject to margin calls because the loss possibilities are unlimited.

All futures positions require margin.

Using options on futures to hedge borrowing costs

Borrowers in the commercial loan market and mortgage market often demand fixed-rate loans.

How can a bank agree to make fixed-rate loans when it has floating-rate liabilities? The bank initially finances the loan by issuing a $1

million 3-month Eurodollar time deposit. After the first three months, the bank expects to

finance the loan by issuing a series of 3-month Eurodollar deposits timed to coincide with the maturity of the preceding deposit.

4/2/02 7/1/02 9/30/02 12/30/02 4/1/03

Issue 3mEuro 2.04%

Issue 3mEuro ?

Issue 3mEuro ?

Issue 3mEuro?

Loan yield 8.0%

Using futures to hedge borrowing costs

Using futures to hedge borrowing costs

Hedging with options on futures

A participant who wants to reduce the risk associated with rising interest rates can buy put options on financial futures. The purchase of a put option essentially places

a cap on the bank’s borrowing cost. If futures rates rise above the strike price plus

the premium on the option, the put will produce a profit that offsets dollar for dollar the increased cost of cash Eurodollars.

If futures rates do not change much or decline, the option may expire unexercised and the bank will have lost a portion or all of the option premium.

Pro

fit

dia

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ms f

or

pu

t op

tion

s o

n E

uro

dollar

futu

res,

A[r

il 2

, 2

00

3Profit

FuturesPrices

96.69(3.31%)

(3.20%)

A. Buy: September 2002 Put Option; Strike Price = 97.25*

Loss

097.25

96.83= Futures Price (F)

F1 = 96.80

-0.56

(4.71%)

Profit

Futures

Prices96.20

(3.80%)

97.25F1 = 95.29

F= 96.21

B. Buy: December 2002 Put Option; Strike Price = 97.25*

Loss

0

-1.05

(5.00%)

F= 95.63

(4.37%)

97.25F1 = 95.00

Profit

FuturesPrices

C. Buy: March 2003 Put Option; Strike Price = 97.25*

Loss

0

-1.62

Buying put options on eurodollar futures to hedge borrowing costs

Buying put options on eurodollar futures to hedge borrowing costs

Interest rate caps, floors and collars

The purchase of a put option on Eurodollar futures essentially places a cap on the bank's borrowing cost.

The advantage of a put option is that for a fixed price, the option premium, the bank can set a cap on its borrowing costs, yet retain the possibility of benefiting from rate declines.

If the bank is willing to give up some of the profit potential from declining rates, it can reduce the net cost of insurance by accepting a floor, or minimum level, for its borrowing cost.

Interest rate caps and floors

Interest rate cap…an agreement between two counterparties that limits the buyer's interest rate exposure to a maximum rate the cap is actually the purchase of a call option

on an interest rate Interest rate floor

…an agreement between two counterparties that limits the buyer's interest rate exposure to a minimum rate the floor is actually the purchase of a put option

on an interest rate

Interest rate cap…A series of consecutive long call options (caplets) on a specific interest rate at the same strike rate.

To establish a Rate Cap: the buyer selects an interest rate index a maturity over which the contract will be in

place a strike (exercise) rate that represents the cap

rate and a notional principal amount By paying an up-front premium, the buyer then

locks-in this cap on the underlying interest rate.

The buyer of a cap receives a cash payment from the seller.The payoff is the maximum of 0 or 3-month LIBOR minus 4% times the notional principal amount.

• If 3-month LIBOR exceeds 4%, the buyer receives cash from the seller and nothing otherwise.

• At maturity, the cap expires.

4 Percent

A. Cap = Long Call Option on 3-Month LIBORDollar Payout(3-month LIBOR

-4%) x NotionalPrincipal Amount

+C

3-MonthLIBOR

B. Cap Payoff: Strike Rate = 4 Percent*

ValueDate

ValueDate

ValueDate

Time

ValueDate

ValueDate

FloatingRate

Rate

4 Percent

The benefits and negatives of buying a cap

Similar to those of buying any option. The bank, as buyer of a cap, can set a

maximum (cap) rate on its borrowing costs. It can also convert a fixed-rate loan to a

floating rate loan. it gets protection from rising rates and retains

the benefits if rates fall. The primary negative to the buyer is that a cap

requires an up-front premium payment. The premium on a cap that is at the money or in

the money in a rising rate environment can be high.

Establish a floor

A bank borrower can establish a floor by selling a call option on Eurodollar futures.

The seller of a call receives the option premium, but agrees to sell to the call option buyer the underlying Eurodollar futures at the agreed strike price upon exercise.

A floor exists because any opportunity gain in the cash market from borrowing at lower rates will be offset by the loss on the sold call option. In essence, the bank has limited its maximum

borrowing cost, but also established a floor borrowing cost.

The combination of setting a cap rate and floor rate is labeled a collar.

A buyer can establish a minimum interest rate by buying a floor on an interest rate index. The buyer of the floor receives a cash payment equal to the greater of zero the product of 4 percent minus 3-month LIBOR and a notional principal amount..

• Thus, if 3-m LIBOR exceeds 6 %, the buyer of a floor at 6% receives nothing.

• The buyer is only paid if 3-m LIBOR is less than 6%

4 Percent

A. Floor = Long Put Option on 3-Month LIBOR

Dollar Payout(4% - 3-month

LIBOR) x NotionalPrincipal Amount

1P

3-MonthLIBOR

ValueDate

ValueDate

ValueDate

Time

B. Floor Payoff: Strike Rate = 4 Percent*

ValueDate

ValueDate

FloatingRate

Rate

4 Percent

Interest rate floor…a series of consecutive floorlets at the same strike rate

To establish a floor, the buyer of an interest rate floor selects an index a maturity for the agreement a strike rate a notional principal amount

By paying a premium, the buyer of the floor, or series of floorlets, has established a minimum rate on its interest rate exposure.

The benefits and negatives of buying a floor

The benefits are similar to those of any put option

A floor protects against falling interest rates while retaining the benefits of rising rates

The primary negative is that the premium may be high on an at the money or in the money floor, especially if the consensus forecast is that interest rates will fall in the future.

Interest rate collar and reverse collar

Interest rate collar…the simultaneous purchase of an interest rate cap and sale of an interest rate floor on the same index for the same maturity and notional principal amount. The cap rate is set above the floor rate.

The objective of the buyer of a collar is to protect against rising interest rates. The purchase of the cap protects against rising

rates while the sale of the floor generates premium income.

A collar creates a band within which the buyer’s effective interest rate fluctuates.

Zero cost collar …requires choosing different cap and floor rates such that the premiums are equal.

Designed to establish a collar where the buyer has no net premium payment.

The benefit is the same as any collar with zero up-front cost.

The negative is that the band within which the index rate fluctuates is typically small and the buyer gives up any real gain from falling rates.

Reverse collar…buying an interest rate floor and simultaneously selling an interest rate cap.

The objective is to protect the bank from falling interest rates. The buyer selects the index rate and matches

the maturity and notional principal amounts for the floor and cap.

Buyers can construct zero cost reverse collars when it is possible to find floor and cap rates with the same premiums that provide an acceptable band.

Caps and floors premium cost

NOTE: Caps/Floors are based on 3-month LIBOR; up-front costs in basis points. Figures in bold print represent strike rates. SOURCE: Bear Stearns

Term Bid Offer Bid Offer Bid OfferCaps1 year 24 30 3 7 1 22 years 81 17 36 43 10 153 years 195 205 104 114 27 345 years 362 380 185 199 86 957 years 533 553 311 334 105 12010 years 687 720 406 436 177 207

Floors1 year 1 2 15 19 57 612 years 1 6 32 39 95 1023 years 7 16 49 58 128 1375 years 24 39 80 94 190 2057 years 40 62 102 116 232 25410 years 90 120 162 192 267 297

1.50% 2.00% 2.50%

A. Caps/Floors

4.00% 5.00% 6.00%

The size of cap and floor premiums are determined by a wide range of factors

The relationship between the strike rate and the prevailing 3-month LIBOR premiums are highest for in the money options and

lower for at the money and out of the money options Premiums increase with maturity.

The option seller must be compensated more for committing to a fixed-rate for a longer period of time.

Prevailing economic conditions, the shape of the yield curve, and the volatility of interest rates. upsloping yield curve -- caps will be more expensive

than floors. the steeper is the slope of the yield curve, ceteris

paribus, the greater are the cap premiums. floor premiums reveal the opposite relationship.

Protecting against falling interest rates

Assume that a bank is asset sensitive such that the bank's net interest income will decrease if interest rates fall. Essentially the bank holds loans priced at

prime +1% and funds the loans with a 3-year fixed-rate deposit at 2.75%.

Three alternative approaches to reduce risk associated with falling rates:

1. entering into a basic interest rate swap to pay 3-month LIBOR and receive a fixed rate

2. buying an interest rate floor3. buying a reverse collar

Using a Basic Swap to Hedge Aggregate Balance Sheet Risk of Loss From Falling Rates

Deposits

Bank

Floating RateLoans

SwapCounterparty

Prime +100

Fixed 2.75

3-m LIBOR

4.55% Fixed

Bank Swap Terms:Pay LIBOR, Receive 4.55%

Buying a floor on a 3-month LIBOR to hedge aggregate balance sheet risk of loss from falling rates

Floor Terms:Buy a 2.0% floor on 3m LIBOR

Deposits

Bank

Floating RateLoans

SwapCounterparty

Prime +100

Fixed 2.75

Receive when3-m LIBOR< 2.0%

Fee: (.21%) /yr

Buying a Reverse Collar to Hedge Aggregate Balance Sheet Risk of Loss From Falling Rates

Strategy: Buy a Floor on a 3-m LIBOR at 1.50%, sell a Cap on 3-m LIBOR at 2.50%

Deposits

Bank

Floating RateLoans

SwapCounterparty

Prime +100

Fixed 2.75

Pay when3-m LIBOR>2.50%

Receive when3-m LIBOR<1.50%

Prem: 0.10% /yr

Protecting against rising interest rates

Assume that the bank has made 3-year fixed rate term loans at 7%, funded via 3-month Eurodollar deposits for which it pays the prevailing LIBOR minus 0.25%. The bank is liability sensitive, it is exposed

to loss from rising interest rates Three strategies to hedge this risk:

1. enter a basic swap to pay 6% fixed-rate and receive 3-month LIBOR

2. buy a cap on 3-month LIBOR with a 5.70% strike rate

3. buy a collar on 3-month LIBOR

Using a basic swap to hedge aggregate balance sheet risk of loss from rising rates

Deposits

Bank

Floating RateLoans

SwapCounterparty

Fixed 7.0%

3-m LIBOR 0.25%

4.56% Fixed

3-m LIBOR

Strategy: Receive 3-m LIBOR, Pay 4.56%

Buying a cap on 3-month LIBOR to hedge aggregate balance sheet risk of loss from rising rates

Strategy: Buy a Cap on 3m LIBOR at 3.0%

Fee: (0.70%) /yr

Deposits

Bank

Floating RateLoans

SwapCounterparty

Fixed 7.0%

3-m LIBOR 0.25%

Receive when3-month LIBOR > 3.00%

Using a collar on 3-month LIBOR to hedge aggregate balance sheet risk of loss from rising rates

Strategy: Buy a Cap at 3.0% and Sell a Floor at 2.0%

Deposits

Bank

Floating RateLoans

SwapCounterparty

Fixed 7.0%

3-m LIBOR 0.25%

Receive when 3-M LIBOR > 3.0%

Pay when 3-M LIBOR < 2.0% Fee: (0.30%) /yr

Interest rate swaps with options

To obtain fixed-rate financing, a firm with access to capital markets has a variety of alternatives:

1. Issue option-free bonds directly2. Issue floating-rate debt that it converts via a basic

swap to fixed-rate debt3. Issue fixed-rate callable debt, and combine this with an

interest rate swap with a call option and a plain vanilla or basic swap

Investors demand a higher rate for callable bonds to compensate for the risk the bonds will be called

the call option will be exercised when interest rates fall, and investors will receive their principal back when similar investment opportunities carry lower yields

the issuer of the call option effectively pays for the option in the form of the higher initial interest rate

Interest rate swap with a call option…like a basic swap except that the call option holder (buyer) has the right to terminate the swap after a set period of time.

Specifically, the swap party that pays a fixed-rate and receives a floating rate has the option to terminate a callable swap prior to maturity of the swap. This option may, in turn, be exercised

only after some time has elapsed.

Exam

ple

: C

allab

le S

wap

Issue fixed-rate debt with an 8-year maturity Dealer spread: 0.10%

Cash Market Alternatives8-year fixed rate debt: 8.50%8-year callable fixed-rate debt: 8.80%6-month floating-rate debt: LIBOR

Interest Rate Swap TermsBasic Swap: 8-year swap without options:

pay 8.55% fixed; receive LIBORpay LIBOR; receive 8.45%

Callable Swap: 8-year swap, callable after 4 yrs:

pay LIBOR; receive 8.90% fixedpay 9.00% fixed; receive LIBOR

Strategy involves three steps implemented simultaneously:

1.issues callable debt at 8.80%2.enters into a callable swap

paying LIBOR and receiving 8.90%

3.enters into a basic swap paying 8.55%, receiving LIBOR.

Net Borrowing Cost after Option ExercisePay: cash rate + callable swap rate + basic swap rate

[8.80% + LIBOR + 8.55%]Receive: callable swap rate + basic swap rate

– [8.90% + LIBOR]Net Pay =8.45%

Net Cost of BorrowingAfter Option Exercise in 4 YrsBasic swap: pay 8.55%; receive LIBORNew floating-rate debt: pay LIBOR +/- ?Net cost = 8.55% +/- spread to LIBOR

Interest rate swap with a put option…A put option gives the holder of a putable swap the right to put the security back to the issuer prior to maturity

With a putable bond an investor can get principal back after a deferment period

Option value increases when interest rates rise Investors are willing to accept lower yields With a putable swap, the party receiving the

fixed-rate payment has the option of terminating the swap after a deferment period, and will likely do so when rates increase.

Exam

ple

: P

uta

ble

Sw

ap

Putable Bond: 8-yr bond, putable after 4 yrs: 8.05% Putable Swap: 8-yr swap, putable after 4 yrs:

pay LIBOR; receive 8.20% fixed pay 8.30% fixed; receive LIBOR

Strategy involves three steps implemented simultaneously:1. issue putable debt at 8.05%2. enter into a putable swap to pay LIBOR and receive 8.20%3. enter into a basic swap to pay 8.55% and receive LIBOR

Net Cost of Borrowing With a Putable Swap for 4 Years Pay: Put bond rate + Put swap rate + Basic swap rate [8.05% + LIBOR + 8.55%] Receive: Put swap rate + Basic swap rate [ 8.20% + LIBOR] Net cost = 8.40%

Net Cost of Borrowing After Option Exercise in 4 Yrs Basic swap: pay 8.55%; receive LIBOR New floating-rate debt: pay LIBOR +/- ? Net cost = 8.55% +/- spread to LIBOR

OPTIONS, CAPS, FLOORS AND MORE COMPLEX SWAPS

Chapter 11

Bank ManagementBank Management, 5th edition.5th edition.Timothy W. Koch and S. Scott MacDonaldTimothy W. Koch and S. Scott MacDonaldCopyright © 2003 by South-Western, a division of Thomson Learning