Study On Pricing Of Interest Rate Derivative Securities

Studying and modeling the dynamic of interest rate and interest rate derivatives represents one of the most challenging topics of finance research since the introduction of option trading on bonds and other interest rate dependent assets. Interest rates exhibit complex stochastic behavior, is mean reversion and are not directly tradable, which means that the dynamic replication strategy is more complex. Empirical studies show that 99% of the dynamic change of different interest rates can be explained by three common factors, which results a number of interest rate models.The basic theories of pricing interest rate derivatives include winner process, Ito process, martingale, differential equation as well as risk-neutral pricing, no-arbitrage principle and assets pricing theorem etc. Stochastic differential equations can be used to resolving the price of interest rate derivatives. It has a canonical equation of interest rate changing with time and its derivative accords with the traded behavior in finance market, but the resolving process is very fussy and difficult and can not receive closed solution in many cases. Martingale is a method that today's price of derivatives is equal to the discounted expectation of its future price if the future expectation is calculated with respect to the risk-neutral probability measure. Martingale is sample than stochastic differential equation and do not involve complex integral, so it is used widely. Numerical analysis methods can resolve the price of derivatives also.There are many studies on models of pricing interest rate derivatives. In general, single factor models are simple and well-specified, but they should not provide a good fit of the data (i.e. be relevant with both interest rate volatility and the term structure's shape). Multi-factors models can make up to the shorts of single factor, but it is difficult to be resolved. Each of these models has its advantages as well as disadvantages.This dissertation mainly makes the following innovation works: 1. Analysing the dynamic behavior of 30 days and 60 days China InterBank Offered Rate, modeling the volatility of 30 days by the family of GARCH models.2.Summarizing the existing models of pricing interest rate derivatives. There are many studies on the pricing from certain way and seldom provide the comprehensive evaluating. In chapter 6 & 7, review a number of popular single factor and multi-factors models. Rather than being exhaustive, we have presented an overview of the most popular models by means of some general characteristics and expose the models one could use.3.Providing a method to price interest rate derivatives by he application of the Principle of Maximum Entropy (PME). PME could maximum results of missing and unknown information. This method is sample and even could use in incomplete markets. The existing models could only use in complete markets.