The Application Of BDT In China's Interest Rate Derivatives Pricing Models

Since the introduction of interest rate derivates trading, interest rates exhibit complex stochastic behavior, it means reversion and are not directly tradable, which means that the dynamic replication strategy is more complex.This article summarizes the basic theories of pricing interest rate derivatives include differential equation, martingale as well as risk-neutral pricing, no-arbitrage principle and assets pricing theorem etc. There are many studies on models of pricing interest rate derivatives. After analyzing equilibrium interest rate models and arbitrage interest rate models comparatively, this article chooses one of arbitrage interest rate models-BDT model as our interest rate pricing derivates model. And based on interest rate special behavior I extend the BDT model by introducing the transition probability parameter. Absorbing the principle of risk-neutral pricing and no-arbitrage, I show that the general dynamic equation arithmetic for which short interest rate satisfies and set up the discrete term structure model for BDT model and its' extend model. Meanwhile I analyze the interest rate swap with these models. The result indicated the BDT model is very suitable for China interest rate swap market, and the model which extend BDT model was better than BDT model on finally demonstration result.This dissertation mainly makes the following innovation works:1,This article summarized the existing models of pricing interest rate derivatives. There are many studies on the pricing from certain way and seldom provide the comprehensive evaluating. But this article reviewed a number of popular equilibrium models and arbitrage models. We have presented an overview of the most popular models by means of some general characteristics and expose the models one could use.2,We use BDT model to pricing interest rate swap firstly, based on interest rate behavior we extend BDT model though introducing the transition probability parameter. Although in some foregoing research these was discussion transition probability parameter in BDT model but is was for bond pricing and the probability parameter adjustment was a little simple.3,When we pricing interest rate swap, we look it as a portfolio of interest rate cap and interest rate floor. That will improve our pricing accuracy when there is not integrated interest rate curve.