Ch30-利率衍生品：短期利率模型Model-of-the-Short-Rate(Hull).pdf

Chapter 30 Interest Rate Derivatives: Model of the Short Rate Options, Futures, and Other Derivatives, 8th Edition, 1 Term Structure Models Black’s model is concerned with describing the probability distribution of a single variable at a single point in time A term structure model describes the evolution of the whole yield curve Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 2 The Zero Curve The process for the instantaneous short rate, r, in the traditional risk-neutral world defines the process for the whole zero curve in this world If P(t, T ) is the price at time t of a zero- coupon bond maturing at time T r ( Tt )  P (t , T) E e  where r is the average r between times t and T Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 3 Equilibrium Models (Risk Neutral World) Rendleman Bartter: dr r dt r dz Vasicek: dr a(b r ) dt dz Cox, Ingersoll, Ross (CIR): dr a(b r ) dt  r dz Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 4 Mean Reversion (Figure 30.1, page 684) Interest rate HIGH interest rate has negative trend Reversion Level