Pricing Derivatives In LIBOR Market Model

It has been ten years since Shanghai Interbank Offered Rate (SHIBOR) been established this year, while its goal to be as a benchmark of the RMB market and to promote the development of Chinese money market has been basically achieved. With Shibor’s developing, the interest rate derivatives based on it has been growing up quickly. The domestic primary interest rate model applied now and numerical analysis method has been unable to adapt the market demand. Researches on pricing derivatives in market model becomes very necessary, under the framework of HJM, LIBOR market model focuses on LIBOR, one interest rate that can be observed in the market, to research term structure of interest rate, which is worldwidely used in the international market. In this paper, through the analysis of the basic theory and application of this model, this paper summarizes pricing application of this model and does a qualitative analysis and comparison.Besides the basic analysis to LIBOR market model, this paper does a research on pricing swaption in LIBOR market model by Monte Carlo simulation analysis method. Before pricing, discretization of the model is crucial, this paper makes a comparison and induction of different discretization method and measurement. Then empirical simulation analysis is been made to confirm which model is the best when it comes to pricing swaption. The main research contents of this paper are listed below.First, based on a detailed discussion on the LIBOR market model, this paper deduces the dynamic process of the forward interest rate of LIBOR under the arbitrage-free principle by spot measure and forward measure. In the meantime, based on the analysis, summary and comparison of the discretization method, Euler method and the two order method, the expression forms of LIBOR market model under different measures and different discretization are derived.Second, using the Monte Carlo simulation method, one of the numerical analysis method to price the interest rate swaption. Thanks to accusable Black price of the derivatives in the LIBOR market model, we use this price as a benchmark to do a comparison of the price bias by simulating the process of pricing swaption.