12.6 The binomial model f 0 (7 0 p)f fer!Ipfi+(l-plfdI p Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.6 The Binomial Model S0u ƒu S0d ƒd S0 ƒ f=e-rT[pfu +(1-p)fd ] p=?
12.7 TThe 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 pOut(I-p)Sod=spe(r-g)r so that q)7 d Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.7 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 ( ) r T q e d p u d − − = −
12.8 Index options Option contracts are on 100X the index The most popular underlying indices are the s&P 100(American)OEX the s&P 500(European) SPX the Major Market Index(XMD Contracts are settled in cash Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.8 Index Options • Option contracts are on 100× the index • The most popular underlying indices are the S&P 100 (American) OEX the S&P 500 (European) SPX the Major Market Index (XMI) • Contracts are settled in cash
12.9 Index Option Exampl oe Consider a call option on the oEX index with a strike price of 560 Suppose 1 contract is exercised When the index level is 580 What is the payoff? (Ans=2000) Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.9 Index Option Example • Consider a call option on the OEX index with a strike price of 560 • Suppose 1 contract is exercised when the index level is 580 • What is the payoff? (Ans=2000)
12.10 Valuing European Index Options We can use the formula for an option on a stock paying a continuous dividend yield Set So current index level Set g average dividend yield expected during the life of the option Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.10 Valuing European Index Options We can use the formula for an option on a stock paying a continuous dividend yield • Set S0 = current index level • Set q = average dividend yield expected during the life of the option