The Chaos Model Of The Term Structure Of Interest Rate And Its Applications To The Pricing Of Interest Rate Derivatives

The thesis discusses the Wiener chaos decomposition model of the term structure of interest rate and its applications to the pricing of interest rate derivatives. This approach was presented by Hughston and Rafailidis recently. The discussion here is around this approach closely. The first chapter of the thesis summarizes the development of term structure of interest rate and gives some basic acknowledges which are used below. The second chapter introduces a general arbitrage-free positive interest model. In this model, the price system of bonds is driven by a Wiener process. The third chapter introduces the Wiener chaos decomposition in Hilbert space L~2(Ω, F, P) and gives its construction method. In the forth chapter, we apply the first and second chaos decomposition to the interest rate model and obtain expression of the price process of zero-coupon bond. The last chapter describes the application of factorisable second chaos model in the pricing of interest rate derivatives and gives some closed-form expressions of the prices of options, caps, floors and swaptions.