Term Structure Models Of Interest Rate And Their Applications In Financing And Policy Decision Problem

Finance mathematics is a new bi-disciplinary science, and is a intersection between mathematics and finance. Their key problems are the choice theory of optimal strategy for investment and the pricing theory of assets. And short interest rate has a determinative importance to the pricing of financial assets and risk managements. So term structure models of interest rate and characteristics of the behavior of interest rate are always a focal point to financial researches. In this paper, recalling the development process about the term structure of interest rate in twenty years, the author wants to get a clear sequence of ideas in all kinds of complicate mathematics models, and gives a brief summary to the major researches achievements in this field. Mainly there are the following contents:First, introduce some conceptions, definitions and relational backgrounds in finance.Second, traditional term structure models of interest rate focus on what the yield curve's shape is and how it forms. The article introduce four theories and compares their characteristics. The research on the modern term structure of interest rate is relative to the pricing of derivatives. Therefore, the paper analyses these models which are often used discrete time and continuous time, combining the problem about the pricing of bond, and gets their advantages and shortcomings in theory.Third, new term structure models of interest rate include some uncertain multi-factors, which the dynamic state of short interest rate depends on the variable about state, and researching the behavior of interest rate by modern mathematical methods. In order to describe the random behavior of interest rate, the essay discusses a series of characteristics about level models based on Chan etc. These models show the relationship between conditional mean and variance of the volatility of interest rate and the level of interest rate. The regime-switching model about interest rate extends Vasicek and CIR models. The essay compares them and finds that the former is more suitable to the behavior of interest rate in China financial market than others. The stochastic process with jumps considers those rare events which have affect on stock price, the pricing of option and so on, the dynamic state of interest rate isdivided into continuous and discontinuous (jumP) processes. The article discusses the dynamic model of interest rate with Poisson process and Levy process in theory, and contrasting with those models under diffusion process. The article gets the former only adds a part with jump, and the model is made up of Ornstein - Uhlenbek process with the characteristic of mean reversion and Poisson process.Fourth, the fundamental thought of martingale method is how to elect a suitable stochastic discounted factor, such that the price of other derivatives divided by discounted factor equals the relative price. According to representation of martingale method of zero-coupon bond, the paper discusses the consistency of term structure of interest rate and how to use them to solve the financing and policy decision problem in enterprise.