期权期货及其衍生品第12弹.ppt

* * * * * * * * * * * * * * * * * * * * * * * * Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 Chapter 12Binomial Trees Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * A Simple Binomial Model A stock price is currently $20 In 3 months it will be either $22 or $18 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Stock Price = $18 Stock Price = $22 Stock price = $20 A Call Option (Figure 12.1, page 254) A 3-month call option on the stock has a strike price of 21. Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Stock Price = $18 Option Price = $0 Stock Price = $22 Option Price = $1 Stock price = $20 Option Price=? Setting Up a Riskless Portfolio For a portfolio that is long D shares and a short 1 call option values are Portfolio is riskless when 22D – 1 = 18D or D = 0.25 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * 22D – 1 18D Valuing the Portfolio(Risk-Free Rate is 12%) The riskless portfolio is: long 0.25 shares short 1 call option The value of the portfolio in 3 months is 22 ×0.25 – 1 = 4.50 The value of the portfolio today is 4.5e–0.12×0.25 = 4.3670 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Valuing the Option The portfolio that is long 0.25 shares short 1 option is worth 4.367 The value of the shares is 5.000 (= 0.25 × 20 ) The value of the option is therefore 0.633 ( 5.000 – 0.633 = 4.367 ) Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Generalization