1. Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 12: Options on Futures My option gave me the right to a futures contract for that much hog [30,000 pounds] until October. Considering the average size of a hog, which I figured to be 500 pounds, this gave me a potential controlling interest in 600 animals. Right then, I vowed to eat more pork chops and bacon, and to call my friends to beg them to do the same. John Rothchild A Fool and His Money 1997

2. Copyright © 2001 by Harcourt, Inc. All rights reserved.2 Important Concepts in Chapter 12 n The concept of an option where the underlying is a futures contract and comparisons to options where the underlying is a spot instrument n Basic principles of pricing options on futures n The early exercise possibilities for American options on futures n The Black and binomial pricing models for options on futures n Trading strategies of buying calls, buying puts and selling covered calls n To compare options on futures with options on the spot

3. Copyright © 2001 by Harcourt, Inc. All rights reserved.3 Characteristics of Options on Futures n Options where exercise establishes either a long or short position in a futures contract at the exercise price u Exercise of long (short) call establishes a long (short) futures. u Exercise of a long (short) put establishes a short (long) futures. n Also called commodity options or futures options.

4. Copyright © 2001 by Harcourt, Inc. All rights reserved.4 Characteristics of Options on Futures (continued) n Example from January 31, 2000. June Treasury bond futures call option with exercise price of 90. u Right to buy June futures at 90 u Costs 3 15/64 or 3.234375, which is $3,234.75. u If exercised when futures = 93, holder establishes long futures position at 90, which is immediately marked to market at 93 for a $3,000 credit to margin account. u Long put works similarly but establishes short futures position. Priced at 1 18/64 or $1,281.25. u Note: expiration can be same month as futures or earlier, depending on the contract.

5. Copyright © 2001 by Harcourt, Inc. All rights reserved.5 Characteristics of Options on Futures (continued) n Many types of options on futures are very actively traded. u See Figure 12.1, p. 507 for annual volume. u See Figure 12.2, p. 508 for market share by contract group. Financials are dominant. u See Table 12.1, p. 12.1 for breakdown by exchange. n See Figure 12.3, p. 510 for The Wall Street Journal quotes. n See Table 12.2, p. 511 for list of contracts trading. n See Table 12.3, p. 512 for most active contracts.

6. Copyright © 2001 by Harcourt, Inc. All rights reserved.6 Pricing Options on Futures n The Intrinsic Value of an American Option on Futures u Minimum value of American call on futures  C a (f 0,T,X)  C a (f 0,T,X)  Max(0,f 0 - X) u Minimum value of American put on futures  P a (f 0,T,X)  P a (f 0,T,X)  Max(0,X - f 0 ) u Difference between option price and intrinsic value is time value.

7. Copyright © 2001 by Harcourt, Inc. All rights reserved.7 Pricing Options on Futures (continued) n The Lower Bound of a European Option on Futures u For calls, construct two portfolios. See Table 12.4, p. 513 u Portfolio A dominates Portfolio B so  C e (f 0,T,X)  C e (f 0,T,X)  Max[0,(f 0 - X)(1+r) -T ] u Note that lower bound can be less than intrinsic value even for calls. u For puts, see Table 12.5, p. 514. u Portfolio A dominates Portfolio B so  P e (f 0,T,X)  P e (f 0,T,X)  Max[0,(X - f 0 )(1+r) -T ]

8. Copyright © 2001 by Harcourt, Inc. All rights reserved.8 Pricing Options on Futures (continued) n Put-Call Parity of Options on Futures u Construct two portfolios, A and B. u See Table 12.6, p. 516. u The portfolios produce equivalent results. Therefore they must have equivalent current values. Thus, F P e (f 0,T,X) = C e (f 0,T,X) + (X - f 0 )(1+r) -T. u Compare to put-call parity for options on spot: F P e (S 0,T,X) = C e (S 0,T,X) - S 0 + X(1+r) -T. F If options on spot and options on futures expire at same time, their values are equal, implying f 0 = S 0 (1+r) T, which we obtained in Chapter 9.

9. Copyright © 2001 by Harcourt, Inc. All rights reserved.9 Pricing Options on Futures (continued) n Early Exercise of Call and Put Options on Futures u Deep in-the-money call may be exercised early because F behaves almost identically to futures F exercise frees up funds tied up in option but requires no funds to establish futures F minimum value of European futures call is less than value if it could be exercised u See Figure 12.4, p. 518. u Similar arguments hold for puts u Compare to the arguments for early exercise of call and put options on spot.

10. Copyright © 2001 by Harcourt, Inc. All rights reserved.10 Pricing Options on Futures (continued) n Options on Futures Pricing Models u Black model for pricing European options on futures

11. Copyright © 2001 by Harcourt, Inc. All rights reserved.11 Pricing Options on Futures (continued) n Options on Futures Pricing Models (continued) u Note that with the same expiration for options on spot as options on futures, this formula gives the same price. u Example F See Table 12.7, p. 520. u Software for Black-Scholes can be used by inserting futures price instead of spot price and risk-free rate for dividend yield. Note why this works. u For puts

12. Copyright © 2001 by Harcourt, Inc. All rights reserved.12 Pricing Options on Futures (continued) n Options on Futures Pricing Models (continued) u Note how the binomial model can be used. u See Figure 12.5, p. 522 for paths of spot and futures price for two-period example with strike of 50. u Futures option prices at expiration (same as spot) F Max(0,156.25 - 100) = 56.25 F Max(0,100 - 100) = 0.0 F Max(0,64 - 100) = 0.0

13. Copyright © 2001 by Harcourt, Inc. All rights reserved.13 Pricing Options on Futures (continued) n Options on Futures Pricing Models (continued) u Option prices at time 1 (futures is 133.75) F [56.25(.6) + 0.0(.4)]/1.07 = 31.54 If American, intrinsic value is 133.75 - 100 = 33.75. So exercise early.If American, intrinsic value is 133.75 - 100 = 33.75. So exercise early. F If futures is 85.60, option is worth nothing u At time 0 option price is F [33.75(.6) + 0.0(.4)] /1.07 = 18.93 Intrinsic value is 114.49 - 100 = 14.49. Do not exercise early. European call would be worth 17.69.Intrinsic value is 114.49 - 100 = 14.49. Do not exercise early. European call would be worth 17.69.

14. Copyright © 2001 by Harcourt, Inc. All rights reserved.14 Trading Strategies for Options on Futures n Buy a Call Option on Futures  Profit equation:  Profit equation:  = Max(0,f T - X) - C   = f T - X - C if f T   = f T - X - C if f T  X   = - C if f T   = - C if f T  X u u See Figure 12.6, p. 525 for December 110 T-bond futures call, C = $1.234375.

15. Copyright © 2001 by Harcourt, Inc. All rights reserved.15 Trading Strategies for Options on Futures (continued) n Buy a Put Option on Futures  Profit equation:  Profit equation:  = Max(0,X - f T ) - P   = - P if f T   = - P if f T  X   = X - f T - P if f T   = X - f T - P if f T  X u u See Figure 12.7, p. 526 for December 110 T-bond futures put, P = $2.515625.

16. Copyright © 2001 by Harcourt, Inc. All rights reserved.16 Trading Strategies for Options on Futures (continued) n Write a Covered Call Option on Futures  Profit equation:  Profit equation:  = f T - f 0 - Max(0,f T - X) + C   = X - f 0 + C if f T   = X - f 0 + C if f T  X   = f T - f 0 + C if f T   = f T - f 0 + C if f T  X u u See Figure 12.8, p. 528 for December 110 T-bond futures covered call, C = $1.234375, f = 108.71875.

17. Copyright © 2001 by Harcourt, Inc. All rights reserved.17 Options on Futures Versus Options on the Spot u With no dividends futures price is always higher than spot price prior to expiration. u So call option on futures is on a higher priced instrument than call option on spot, but F This applies to American calls only because European calls cannot be exercised until expiration. u Similar line of reasoning applies to puts on futures. u Futures options are the only exchange-listed options that trade side-by-side with the underlying instrument. u Easier to transact in the underlying when it is a futures than when it is a stock index.

18. Copyright © 2001 by Harcourt, Inc. All rights reserved.18 Summary See Figure 12.9, p. 531. Appendix 12. Selected Options on Futures Contract Specifications