期权,期货及其衍生品第9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 29Quanto, Timing, and Convexity Adjustments Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Forward Yields and Forward Prices We define the forward yield on a bond as the yield calculated from the forward bond price There is a non-linear relation between bond yields and bond prices It follows that when the forward bond price equals the expected future bond price, the forward yield does not necessarily equal the expected future yield Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Relationship Between Bond Yields and Prices (Figure 29.1, page 669) Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Bond Price Yield Y3 B 1 Y1 Y2 B 3 B 2 Convexity Adjustment for Bond Yields (Eqn 29.1, p. 670) Suppose a derivative provides a payoff at time T dependent on a bond yield, yT observed at time T. Define: G(yT) : price of the bond as a function of its yield y0 : forward bond yield at time zero sy : forward yield volatility The expected bond price in a world that is FRN wrt P(0,T) is the forward bond price The expected bond yield in a world that is FRN wrt P(0,T) is Options, Futures, and Other Derivatives, 8th Edition, Copyright ? John C. Hull 2012 * Convexity Adjustment for Swap Rate The expected value of the swap rate for the period T to T+t in a world that is FRN wrt P(0,T) is (approximately) where G(y) defines the relationship between price and yield for a bond lasting between T and T+t that pays a coupon equal to the forward swap rate Options, Futures, and Other Deri