Interest-Rate Derivatives Pricing Based On One-Factor HJM Model

A large flow of financial products are emerged and become an important part of the financial markets in recent 30 years. According to the statistics, The volume of the interest-rate derivatives increases rapidly and has accounted for more than 95 percent of the financial derivatives. Therefore, it is most necessary for us to do research about interest-rate derivatives. According to a brief variety of products trading on the Chinese market, most of scholars price the products in generally with junior models, such as the Black-Scholes model,but the result showed that the method is not accurate. Heath-Jarrow-Morton model as a model of one of the no-arbitrary models has a deep application weather in theory or in practice abroad.This model is popular for the traders to develop and price the interest-rate derivatives.After summarize the conditions of the HJM model,this paper do research in parameter estimation for two kinds of volatility functions.We also price the bonds nested with option,which developed by China Development Bank.After review the research at home and aboard, we summarizes the basic theory both in the static models and the dynamic models.With the consideration of the actual conditions of our market of interest-rate derivatives, we compare two compete HJM models on the basis of how well they price the bonds nested with option.The aim of this paper is to provide a valid model to price the bond with option for the traders. This article mainly makes the following work:First,after analyzing the theory of the HJM model in details,this paper proposes and deduct the HJM binomial tree in risk-neutral word without arbitrage.Then based on the data of national bonds traded in the shanghai stock market, we first use generalized method of moments for the parameter estimation in the constant volatility function model and exponential decay volatility function model separately.The results indicate that the exponential decay volatility function model is equivalent to another constant volatility function model for a short time as its decay rate is so small.Second we compare two one-factor HJM models, which with two different volatility function, according to how well they price the bonds with option.In the implement process, we first use the NSS model to get the term structure of forward interest rate,then pricing the nine puttable bonds and three callable bond using the HJM binomial tree.Overall the one-factor HJM model with the constant volatility shows better,and it is suitable to do research in the Chinese market.