The Binomial Tree Model In Pricing Securities With Stochastic Interest Rates

In financial mathematics the pricing of securities is an important and meaningful issues which is of both theoretical and practical value,and has always been one of issues in Chinese security market . In the fields of the study of pricing of derivative securities with interest rate being a constant or fixed works in concern with the situation when the interest rate being stochastic are less,but the variants of price and interest rate which the value of securities depended upon are always some stochastic process with uncertain changing features. Theofore the study of securities pricing which based on the model of random interest rate meets the practical demand. The paper is of security pricing with binomial tree model,use it to price the securities with stochastic rate.The whole thesis is consists of four chapters as follows:IN CHAPTER ONE: we introduce the background and current development of the pricing of securities, particularly, we describe the binomial tree model and rate model.The rate model includes the simple discrete-time rate model and continues rate model,in the end describe the main results of the paper.IN CHAPTER TWO: the binomial tree model of the band pricing with stochastic interest rate.we introduce two classical models,Ho-Lee model and Vasicek model,by the process of the two models, we can know how to deal with the rate when it is stochastic,if the interest rate is stochastic we suppose that the rate follow the Ho-Lee model or Vasicek model, and we can get the zero coupon bond prices.IN CHAPTER THREE:the derivative pricing with stochastic interest rate, after giving the common option pricing and the formula call option pricing with extensive Vasicek model,the chapter begins to price the European call option American options and a few of kinds of exotic options.IN CHAPTER FOUR: the binomial tree model of defaultable securities with stochastic interest, because many famous companies may bankrupt, it is realistic meaning to consider the pricing of defaultable securities,we mainly consider the discrete-time interest rates term structure model for the pricing of defaultable securities, particularly, considering the default-able compensate stochastic.