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1、Chapter 17Futures Options,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,1,Options on Futures,Referred to by the maturity month of the underlying futures The option is American and usually expires on or a few days before the earliest delivery date of the underlying futu
2、res contract,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,2,Mechanics of Call Futures Options,When a call futures option is exercised the holder acquires A long position in the futures A cash amount equal to the excess of the futures price at the time of the most rece
3、nt settlement over the strike price,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,3,Mechanics of Put Futures Option,When a put futures option is exercised the holder acquires A short position in the futures A cash amount equal to the excess of the strike price over the
4、 futures price at the time of the most recent settlement,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,4,Example 1(page 361),Dec.call option contract on copper futures has a strike of 240 cents per pound.It is exercised when futures price is 251 cents and most recent s
5、ettlement is 250.One contract is on 250,000 poundsTrader receivesLong Dec.futures contract on copper$2,500 in cash,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,5,Example 2(page 362),Dec put option contract on corn futures has a strike price of 400 cents per bushel.It
6、is exercised when the futures price is 380 cents per bushel and the most recent settlement price is 379 cents per bushel.One contract is on 5000 bushelsTrader receives Short Dec futures contract on corn$1,050 in cash,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,6,The
7、Payoffs,If the futures position is closed out immediately:Payoff from call=F KPayoff from put=K Fwhere F is futures price at time of exercise,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,7,Potential Advantages of Futures Options over Spot Options,Futures contracts may
8、 be easier to trade and more liquid than the underlying assetExercise of option does not lead to delivery of underlying assetFutures options and futures usually trade on same exchangeFutures options may entail lower transactions costs,Options,Futures,and Other Derivatives,8th Edition,Copyright John
9、C.Hull 2012,8,European Futures Options,European futures options and spot options are equivalent when futures contract matures at the same time as the option It is common to regard European spot options as European futures options when they are valued in the over-the-counter markets,Options,Futures,a
10、nd Other Derivatives,8th Edition,Copyright John C.Hull 2012,9,Put-Call Parity for Futures Options(Equation 16.1,page 345),Consider the following two portfolios:1.European call plus KerT of cash 2.European put plus long futures plus cash equal to F0erT They must be worth the same at time T so thatc+K
11、erT=p+F0erT,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,10,Other Relations,F0 erT K(F0 K)erTp(F0 K)erT,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,11,Binomial Tree Example,A 1-month call option on futures has a strike price of 29.,Opt
12、ions,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,12,Futures Price=$28Option Price=$0,Setting Up a Riskless Portfolio,Consider the Portfolio:long D futuresshort 1 call optionPortfolio is riskless when 3D 4=2D or D=0.8,Options,Futures,and Other Derivatives,8th Edition,Copyrigh
13、t John C.Hull 2012,13,Valuing the Portfolio(Risk-Free Rate is 6%),The riskless portfolio is:long 0.8 futuresshort 1 call optionThe value of the portfolio in 1 month is 1.6The value of the portfolio today is 1.6e0.06/12=1.592,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 201
14、2,14,Valuing the Option,The portfolio that is long 0.8 futuresshort 1 option is worth 1.592The value of the futures is zeroThe value of the option must therefore be 1.592,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,15,Generalization of Binomial Tree Example(Figure 17
15、.2,page 368),A derivative lasts for time T and is dependent on a futures price,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,16,Generalization(continued),Consider the portfolio that is long D futures and short 1 derivativeThe portfolio is riskless when,Options,Futures,
16、and Other Derivatives,8th Edition,Copyright John C.Hull 2012,17,F0u D-F0 D u,F0d D-F0D d,Generalization(continued),Value of the portfolio at time T is F0u D F0D uValue of portfolio today is Hence=F0uD F0D uerT,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,18,Generaliza
17、tion(continued),Substituting for D we obtain=p u+(1 p)d erT where,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,19,Growth Rates For Futures Prices,A futures contract requires no initial investmentIn a risk-neutral world the expected return should be zeroThe expected gr
18、owth rate of the futures price is therefore zeroThe futures price can therefore be treated like a stock paying a dividend yield of r,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,20,Valuing European Futures Options,We can use the formula for an option on a stock paying
19、 a dividend yieldS0=current futures price,F0q=domestic risk-free rate,r Setting q=r ensures that the expected growth of F in a risk-neutral world is zeroThe result is referred to as Blacks model because it was first suggested in a paper by Fischer Black in 1976,Options,Futures,and Other Derivatives,
20、8th Edition,Copyright John C.Hull 2012,21,Blacks Model(Equations 17.9 and 17.10,page 370),Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,22,How Blacks Model is Used in Practice,Blacks model is frequently used to value European options on the spot price of an asset in th
21、e over-the-counter marketThis avoids the need to estimate income on the asset,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,23,Using Blacks Model Instead of Black-Scholes-Merton(Example 17.7,page 371),Consider a 6-month European call option on spot gold6-month futures
22、price is 1,240,6-month risk-free rate is 5%,strike price is 1,200,and volatility of futures price is 20%Value of option is given by Blacks model with F0=1,240,K=1,200,r=0.05,T=0.5,and s=0.2It is 88.37,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,24,Futures Option Pric
23、e vs Spot Option Price,If futures prices are higher than spot prices(normal market),an American call on futures is worth more than a similar American call on spot.An American put on futures is worth less than a similar American put on spot.When futures prices are lower than spot prices(inverted mark
24、et)the reverse is true.,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,25,Futures Style Options(page 372-73),A futures-style option is a futures contract on the option payoffSome exchanges trade these in preference to regular futures optionsThe futures price for a call
25、futures-style option isThe futures price for a put futures-style option is,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,26,Put-Call Parity Results,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,27,Summary of Key Results from Chapters 16 and 17,We can treat stock indices,currencies,and futures like a stock paying a dividend yield of qFor stock indices,q is average dividend yield on the index over the option lifeFor currencies,q=rFor futures,q=r,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,28,
