CH22HullOFOD5Ebw.pptVIP

Interest Rate Derivatives: The Standard Market ModelsChapter 22 Why Interest Rate Derivatives are Much More Difficult to Value Than Stock Options We are dealing with the whole term structure of interest rates; not a single variable The probabilistic behavior of an individual interest rate is more complicated than that of a stock price Why Interest Rate Derivatives are Much More Difficult to Value Than Stock Options Volatilities of different points on the term structure are different Interest rates are used for discounting as well as for defining the payoff Main Approaches to PricingInterest Rate Options Use a variant of Black抯 model Use a no-arbitrage (yield curve based) model Black抯 Model Its Extensions Black抯 model is similar to the Black-Scholes model used for valuing stock options It assumes that the value of an interest rate, a bond price, or some other variable at a particular time T in the future has a lognormal distribution Black抯 Model Its Extensions(continued) The mean of the probability distribution is the forward value of the variable The standard deviation of the probability distribution of the log of the variable is where s is the volatility The expected payoff is discounted at the T-maturity rate observed today Black抯 Model (Eqn 22.1 and 22.2, p 509) K : strike price F0 : forward value of variable T : option maturity s : volatility The Black抯 Model: Payoff Later Than Variable Being Observed K : strike price F0 : forward value of variable s : volatility T : time when variable is observed T * : time of payoff Validity of Black抯 Model Black抯 model appears to make two approximations: 1. The expected value of the underlying variable is assumed to be its forward price 2. Interest rates are assumed to be constant for discounting We will see that these assumptions offset each other European Bond Options When valuing European bond options it is usual to assume that the