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Options option valuation

determinants of option pricing; option price

sensitivities option trading strategies

the Greek letters

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Derivative securities as a whole have becomeincreasingly important in the management ofrisk and this chapter details the use of options

in that vein. A review of basic options puts and calls is

followed by a discussion of fixed-income, orinterest rate options. The chapter also explains

options that address foreign exchange risk,credit risks

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Long position in an option is synonymouswith: Holder, buyer, purchaser, the long Holder of an option has the right, but not the

obligation to exercise the option

Short position in an option is synonymouswith: Writer, seller, the short Obliged to fulfill terms of the option if the option

holder chooses to exercise.

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A call provides the holder (or long position)with the right, but not the obligation, topurchase an underlying security at a pre-specified exerciseor strikeprice. Expiration date: American and European options

The purchaser of a call pays the writer of thecall (or the short position) a fee, or callpremiumin exchange.

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If the price of the bond underlying the calloption rises above the exercise price, bymore than the amount of the premium, thenexercising the call generates a profit for the

holder of the call.

Since bond prices and interest rates move inopposite directions, the purchaser of a callprofits if interest rates fall.

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Zero-sum game: The writer of a call (short call position) profits when

the call is not exercised (or if the bond price is notfar enough above the exercise price to erode theentire call premium).

Gains for the short call position are losses for thelong call position.

Gains for the long call position are losses for the

short call position.

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Since the price of the bond could rise to equalthe sum of the principal and interestpayments (zero rate of interest), the writer ofa call is exposed to the risk of very largelosses.

Recall that losses to the writer are gains tothe purchaser of the call. Therefore, potentialprofit to call purchaser could be very large.(Note that call options on stocks have no

theoretical payoff limit at all). Maximum gain for the writer occurs if bondprice falls below exercise price.

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Buy a call Write a call

X

X

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A put provides the holder (or long position)with the right, but not the obligation, to sellan underlying security at a prespecifiedexerciseor strikeprice. Expiration date: American and European options

The purchaser of a put pays the writer of theput (or the short position) a fee, or putpremiumin exchange.

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If the price of the bond underlying the putoption falls below the exercise price, by morethan the amount of the premium, thenexercising the put generates a profit for the

holder of the put.

Since bond prices and interest rates move inopposite directions, the purchaser of a putprofits if interest rates rise.

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Zero-sum game: The writer of a put (short put position) profits when

the put is not exercised (or if the bond price is notfar enough below the exercise price to erode the

entire put premium). Gains for the short position are losses for the long

position. Gains for the long position are losses forthe short position.

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Since the bond price cannot be negative, themaximum loss for the writer of a put occurswhen the bond price falls to zero. Maximum loss = exercise price minus the premium

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Buy a Put Write a Put(Long Put) (Short Put)

X

X

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Many smaller FIs constrained to buyingrather than writing options. Economic reasons

Potentially large downside losses for calls.

Potentially large losses for puts Gains can be no greater than the premiums so less

satisfactory as a hedge against losses in bondpositions

Regulatory reasons

Risk associated with writing naked options.

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Hedging with futures eliminates bothupsideand downside

Hedging with options eliminates risk in onedirection only

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Hedging with Futures

Bond Portfolio

Bond Price

PurchasedFuturesContract

X

0

Gain

Loss

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Weaknesses of Black-Scholes model. Assumes short-term interest rate constant

Assumes constant variance of returns on underlyingasset.

Behavior of bond prices between issuance andmaturity

Pull-to-par.

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Credit spread call option Payoff increases as (default) yield spread on a

specified benchmark bond on the borrowerincreases above some exercise spread S.

Digital default option Pays a stated amount in the event of a loan default.

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Chicago Board of Trade www.cbot.comCBOE www.cboe.com

Chicago Mercantile Exchange www.cme.com

Wall Street Journal www.wsj.com

http://www.cbot.com/http://www.cboe.com/http://www.cme.com/http://www.wsj.com/http://www.wsj.com/http://www.cme.com/http://www.cboe.com/http://www.cbot.com/