期权,期货及其衍生品.ppt

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 Alternatives for Handling Interest Rates Duration approach: Linear relation between DP and Dy but assumes parallel shifts) Cash flow mapping: Cash flows are mapped to standard maturities and variables are zero-coupon bond prices with the standard maturities Principal components analysis: 2 or 3 independent shifts with their own volatilities * When Linear Model Can be Used Portfolio of stocks Portfolio of bonds Forward contract on foreign currency Interest-rate swap Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * The Linear Model and Options Consider a portfolio of options dependent on a single stock price, S. If d is the delta of the option, then it is approximately true that Define Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Linear Model and Options continued (equations 20.3 and 20.4) Then Similarly when there are many underlying market variables where di is the delta of the portfolio with respect to the ith asset Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Example Consider an investment in options on Microsoft and ATT. Suppose the stock prices are 120 and 30 respectively and the deltas of the portfolio with respect to the two stock prices are 1,000 and 20,000 respectively As an approximation where Dx1 and Dx2 are the percentage changes in the two stock prices Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 But the distribution of the daily return on an option is not normal  The linear model fails to capture skewness in the probability distribution of the portfolio value. * Impact of gamma (Figure 21.4, page 486) Options, Futures, an