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