1. 13.1 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Options on Futures Chapter 13

2. 13.2 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Potential Advantages of Futures Options over Spot Options Futures contract may be easier to trade than underlying asset Exercise of the option does not lead to delivery of the underlying asset Futures options and futures usually trade in adjacent pits at exchange Futures options may entail lower transactions costs

3. 13.3 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Mechanics of Call Futures Options When a call futures option is exercised the holder acquires 1. A long position in the futures 2. A cash amount equal to the excess of the futures price over the strike price

4. 13.4 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Mechanics of Put Futures Option When a put futures option is exercised the holder acquires 1. A short position in the futures 2. A cash amount equal to the excess of the strike price over the futures price

5. 13.5 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull The Payoffs If the futures position is closed out immediately: Payoff from call = F-X Payoff from put = X-F where F is futures price at time of exercise

6. 13.6 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Problem An investor buys a July call futures option contract on gold. The contract size is 100 ounces. The strike price is 500. The investor exercise when the gold futures price is 540 and the most recent settlement price is 538. Calculate the payoff from the exercise decision.

7. 13.7 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Problem An investor buys a September put futures option contract on corn. The contract size is 5,000 bushels. The strike price is 200 cents. The investor exercises when the September corn futures price is 180 and the most recent settlement price is 179. Calculate the total payoff from the exercise decision.

8. 13.8 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Put-Call Parity for Futures Options Consider the following two portfolios: 1. European call plus Xe -rT of cash 2. European put plus long futures plus cash equal to Fe -rT They must be worth the same at time T so that c+Xe -rT =p+Fe -rT

9. 13.9 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Other Relations Fe -rT -X < C -P < F-Xe -rT c > (F-X)e -rT p > (F-X)e -rT

10. 13.10 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Problem Suppose that a future price is currently trading at 35. A European call option and a European put option on the futures with a strike price of 34 are both priced at 2 in the market today. The risk-free interest rate is 10 percent annum. Identify an arbitrage opportunity.

11. 13.11 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull European Options on Stocks Paying Continuous Dividends We get the same probability distribution for the stock price at time T in each of the following cases: 1.The stock starts at price S & provides a continuous dividend yield = q 2.The stock starts at price S e –q T & provides no income

12. 13.12 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Extension of Chapter 11 Results (Eqns 12.4, 12.5, p274)

13. 13.13 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Valuing European Futures Options We can use the formula for an option on a stock paying a continuous dividend yield Set S = current futures price (F ) Set q = domestic risk-free rate (r ) Setting q = r ensures that the expected growth of F in a risk-neutral world is zero

14. 13.14 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Growth Rates For Futures Prices A futures contract requires no initial investment In a risk-neutral world the expected return should be zero The expected growth rate of the futures price is therefore  zero The futures price can therefore be treated like a stock paying a dividend yield of r

15. 13.15 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Black’s Formula The formulas for European options on futures are known as Black’s formulas

16. 13.16 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Futures Option Prices vs Spot Option Prices 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 market) the reverse is true

17. 13.17 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Problem Consider a European put futures option on crude oil. The time to maturity is four months, the current futures price is $20, the exercise price is $20, the risk free interest rate is 9 percent per annum, and the volatility of the futures price is 25 percent per annum.