《金融期货与期权》（英文版） Chapter 13 Stock Indices, Currencies, and Futures

13.1 Options on Stock Indices. Currencies and Futures Chapter 13 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.1 Options on Stock Indices, Currencies, and Futures Chapter 13

European Options on Stocks 13.2 Providing a dividend yield 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 So and provides a dividend yield= q 2. The stock starts at price Soe q/ and provides no income Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.2 European Options on Stocks Providing a Dividend Yield 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 S0 and provides a dividend yield = q 2. The stock starts at price S0 e –q T and provides no income

European Options on Stocks 13.3 Providing dividend yield continued We can value European options by reducing the stock price to soe q/ and then behaving as though there is no dividend Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.3 European Options on Stocks Providing Dividend Yield continued We can value European options by reducing the stock price to S0 e –q T and then behaving as though there is no dividend

13.4 Extension of Chapter 8 Results (Equations 13.1 to 13.3) Lower bound for calls c≥Sey-Ker7 Lower bound for puts T p≥Ke-S q T 已 Put Call Parity Ctke=p+seat Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.4 Extension of Chapter 8 Results (Equations 13.1 to 13.3) q T r T c S e Ke − −  0 − Lower Bound for calls: Lower Bound for puts r T qT p Ke S e − −  − 0 Put Call Parity r T q T c Ke p S e − − + = + 0

Extension of Chapter 12 3.5 Results(equations 13.4 and 14.5) c=Soe n(du-ke n(d2) p=ke N(d2)-soe(dI /2)T where d, l(S/K)+(-q+o2 ln(S/K)+(r-q-2/2)T T Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.5 Extension of Chapter 12 Results (Equations 13.4 and 14.5) T S K r q T d T S K r q T d p K e N d S e N d c S e N d K e N d r T q T q T r T  + − −  =  + − +  = = − − − = − − − − − / 2) 2 ln( / ) ( / 2) 2 ln( / ) ( ( ) ( ) ( ) ( ) 0 2 0 1 2 0 1 0 1 2 where

13.6 The binomial model f 0 f=e-lpf +(l-plfdl Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.6 The Binomial Model S0u ƒu S0d ƒd S0 ƒ f=e-rT[pfu +(1-p)fd ]

13.7 The binomial model continued In a risk-neutral world the stock price grows at r-g rather than at r when there is a dividend yield at rate q The probability, p, of an up movement must therefore satisfy ou+(1-p)Sod=Soe(r-g) so that lqr Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.7 The Binomial Model continued • In a risk-neutral world the stock price grows at r-q rather than at r when there is a dividend yield at rate q • The probability, p, of an up movement must therefore satisfy pS0u+(1-p)S0d=S0 e (r-q)T so that p e d u d r q T = − − ( − )

138 Index options Option contracts are on 100 times the index The most popular underlying indices are the Dow Jones Industrial(European DJX the S&P 100(American)OEX the S&P 500(European ) SPX Contracts are settled in cash Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.8 Index Options • Option contracts are on 100 times the index • The most popular underlying indices are – the Dow Jones Industrial (European) DJX – the S&P 100 (American) OEX – the S&P 500 (European) SPX • Contracts are settled in cash

13.9 Index option Example Consider a call option on an index with a strike price of 560 Suppose 1 contract is exercised When the index level is 580 What is the payoff? Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.9 Index Option Example • Consider a call option on an index with a strike price of 560 • Suppose 1 contract is exercised when the index level is 580 • What is the payoff?

13.10 Using Index options for Portfolio insurance Suppose the value of the index is So and the strike price is K If a portfolio has a B of 1.0, the portfolio insurance is obtained by buying 1 put option contract on the index for each 100S dollars held If the B is not 1.0, the portfolio manager buys B put options for each 100So dollars held In both cases, K is chosen to give the appropriate insurance level Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 13.10 Using Index Options for Portfolio Insurance • Suppose the value of the index is S0 and the strike price is K • If a portfolio has a b of 1.0, the portfolio insurance is obtained by buying 1 put option contract on the index for each 100S0 dollars held • If the b is not 1.0, the portfolio manager buys b put options for each 100S0 dollars held • In both cases, K is chosen to give the appropriate insurance level