Options-Futures-and-Other-Derivatives-8t-CH16-17讲义设计.ppt

* Generalization(continued) Value of the portfolio at time T is F0u D –F0D – ?u Value of portfolio today is – ? Hence ? = – [F0u D –F0D – ?u]e-rT * Generalization(continued) Substituting for D we obtain ? = [ p ?u + (1 – p )?d ]e–rT where * Valuing European Futures Options We can use the formula for an option on a stock paying a dividend yield Set S0 = current futures price (F0) Set q = domestic risk-free rate (r ) Setting q = r ensures that the expected growth of F in a risk-neutral world is zero * Black’s Formula (Equations 17.9 and 17.10, page 370) The formulas for European options on futures are known as Black’s formulas * Summary of Key Results We can treat stock indices, currencies, and futures like a stock paying a dividend yield of q For stock indices, q = average dividend yield on the index over the option life For currencies, q = r? For futures, q = r * * * 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 Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Chapter 16Options on Stock Indices and CurrenciesChapter 17Futures Options Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * * European Options on StocksProviding 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 S0e–q T and provides no income * European Options on StocksProviding Dividend Yieldcontinued We can value European options by reducing the stock price to S0e–q T and then behaving as though there is no d