Finance Chapter Twenty | Course Paper

Chapter Twenty Five

Options, Caps, Floors, and Collars

Chapter Outline

Introduction

Basic Features of Options

Buying a Call Option on a Bond

Writing a Call Option on a Bond

Buying a Put Option on a Bond

Writing a Put Option on a Bond

Writing versus Buying Options

Economic Reasons for Not Writing Options

Regulatory Reasons

Futures versus Options Hedging

The Mechanics of Hedging a Bond or Bond Portfolio

Hedging with Bond Options Using the Binomial Model

Actual Bond Options

Using Options to Hedge Interest Rate Risk on the Balance Sheet

Using Options to Hedge Foreign Exchange Risk

Hedging Credit Risk with Options

Hedging Catastrophe Risk with Call Spread Options

Caps, Floors, and Collars

Caps

Floors

Collars

Caps, Floors, Collars, and Credit Risk

Summary

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Solutions to End-of-Chapter Questions and Problems: Chapter Twenty Five

1. How does using options differ from using forward or futures contracts?

Both options and futures contracts are useful in managing risk. Other than the pure mechanics,

the primary difference between these contracts lies in the requirement of what must be done on

or before maturity. Futures and forward contracts require that the buyer or seller of the contracts

must execute some transaction. The buyer of an option has the choice to execute the option or to

let it expire without execution. The writer of an option must perform a transaction only if the

buyer chooses to execute the option.

2. What is a call option?

A call option is an instrument that allows the owner to buy some underlying asset at a

prespecified price on or before a specified maturity date.

3. What must happen to interest rates for the purchaser of a call option on a bond to make

money? How does the writer of the call option make money?

The call option on a bond allows the owner to buy a bond at a specific price. For the owner of

the option to make money, he should be able to immediately sell the bond at a higher price.

Thus, for the bond price to increase, interest rates must decrease between the time the option is

purchased and the time it is executed. The writer of the call option makes a premium from the

sale of the option. If the option is not exercised, the writer maximizes profit in the amount of the

premium. If the option is exercised, the writer stands to lose a portion or the entire premium, and

may lose additional money if the price on the underlying asset moves sufficiently far.

4. What is a put option?

A put option is an instrument that allows the owner to sell some underlying asset at a

prespecified price on or before a specified maturity date.

5. What must happen to interest rates for the purchaser of a put option on a bond to make

money? How does the writer of the put option make money?

The put option on a bond allows the owner to sell a bond at a specific price. For the owner of the

option to make money, he should be able to buy the bond at a lower price immediately prior to

exercising the option. Thus, for the bond price to decrease, interest rates must increase between

the time the option is purchased and the time it is executed. The writer of the put option makes a

premium from the sale of the option. If the option is not exercised, the writer maximizes profit

in the amount of the premium. If the option is exercised, the writer stands to lose a portion or the

entire premium, and may lose additional money if the price on the underlying asset moves

sufficiently far.

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6. Consider the following:

a. What are the two ways to use call and put options on T-bonds to generate positive cash

flows when interest rates decline? Verify your answer with a diagram.

The FI can either (a) buy a call option, or (b) sell a put option on interest rate instruments,

such as T-bonds, to generate positive cash flows in the event that interest rates decline. In

the case of a call option, positive cash flows will increase as long as interest rates continue

to decrease. See Figure 25-1 in the text as an example of positive cash flows minus the

premium paid for the option. Although not labeled in this diagram, interest rates are

assumed to be decreasing as you move from left to right on the x-axis. Thus bond prices

are increasing.

The sale of a put option generates positive cash flows from the premium received. Figure

25-4 shows that the payoff will decrease as the price of the bond falls. Of course this can

only happen if interest rates are increasing. Again, although not labeled in this diagram,

interest rates are assumed to be increasing as you move from right to left on the x-axis.

b. Under what balance sheet conditions can an FI use options on T-bonds to hedge its

assets and/or liabilities against interest rate declines?

An FI can use call options on T-bonds to hedge an underlying cash position that decreases

in value as interest rates decline. This would be true if, in the case of a macrohedge, the

FI’s duration gap is negative and the repricing gap is positive. In the case of a microhedge,

the FI can hedge a single fixed-rate liability against interest rate declines.

c. Is it more appropriate for FIs to hedge against a decline in interest rates with long calls

or short puts?

An FI is better off purchasing calls as opposed to writing puts for two reasons. First,

regulatory restrictions limit an FI’s ability to write naked short options. Second, since the

potential positive cash inflow on the short put option is limited to the size of the put

premium, there may be insufficient cash inflow in the event of interest rate declines to

offset the losses in the underlying cash position.

7. In each of the following cases, identify what risk the manager of an FI faces and whether

the risk should be hedged by buying a put or a call option.

a. A commercial bank plans to issue CDs in three months.

The bank faces the risk that interest rates will increase. The FI should buy a put option. If

rates rise, the CDs can be purchased at a lower price and sold immediately by exercising

the option. The gain will offset the higher interest rate the FI must pay in the spot market.

b. An insurance company plans to buy bonds in two months.

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The insurance company (IC) is concerned that interest rates will fall, and thus the price of

the bonds will rise. The IC should buy call options that allow the bond purchase at the

lower price. The bonds purchased with the options can be sold immediately for a gain that

can be applied against the lower yield realized in the market. Or the bonds can be kept and

placed in the IC’s portfolio if they are the desired type of asset.

c. A thrift plans to sell Treasury securities next month.

The thrift is afraid that rates will rise and the value of the bonds will fall. The thrift should

buy a put option that allows the sale of the bonds at or near the current price.

d. A U.S. bank lends to a French company with a loan payable in francs.

The U.S. bank is afraid that the dollar will appreciate (francs will depreciate). Thus the

bank should buy a put to sell francs at or near the current exchange rate.

e. A mutual fund plans to sell its holding of stock in a British company.

The fund is afraid that the dollar will appreciate (£ will depreciate). Thus the fund should

buy a put to sell £ at or near the current exchange rate.

f. A finance company has assets with a duration of six years and liabilities with a duration

of 13 years.

The FI is concerned that interest rates will fall, causing the value of the liabilities to rise

more than the value of the assets which would cause the value of the equity to decrease.

Thus the bond should buy a call option on interest rates (bonds).

8. Consider an FI that wishes to use bond options to hedge the interest rate risk in the bond

portfolio.

a. How does writing call options hedge the risk when interest rates decrease?

In the case where the FI is long the bond, writing a call option will provide extra cash flow

in the form of a premium. But falling interest rates will cause the value of the bond to

increase, and eventually the option will be exercised at a loss to the writer. But the loss is

offset by the increase in value of the long bond. Thus the initial goal of maintaining the

interest rate return on the long bond can be realized.

b. Will writing call options fully hedge the risk when interest rates increase? Explain.

Writing call options provides a premium that can be used to offset the losses in the bond

portfolio caused by rising rates up to the amount of the premium. Further losses are not

protected.

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c. How does buying a put option reduce the losses on the bond portfolio when interest

rates rise?

When interest rates increase, the value of the bond falls, but the put allows the sale of the