Pricing Of Financial Derivatives Under Stochastic Interest Rate

The theory and practice of derivative securities have been developed very fast in the recent twenty years all over the world. Many mathematical scientists and financial economists pay more and more attention to the problems on options and investment,consumption.Since 1973,in which Fischer Black and Myron Scholes proposed a famous option pricing model - Black-Scholes model,option pricing theory has developed quickly. Recently, in addition to known European options and American options, there appear many new variety which are changed,composed,derived by vanilla options in international financial market. Option pricing theory,the important part of modern finance,has promoted the prosperity of financial market. Together with the portfolio selection theory, the capital asset pricing theory,the effectiveness theory of market and acting issue ,it is regarded as one of the five theory modules in modern finance.In this paper,we study the pricing issue of the exchange option under stochastic interest rate, we explore the issue of pricing issue of exchange option and gain material conclusion. The major work is supported by principles of stochastic analysis with the ides of financial engineering. And this thesis is composed of the following five chapters:In chapter 1,the significance,origin,development,academic trends and research methods of option pricing and the main contents of this thesis are introduced.In chapter 2,the paper summarizes the basal pricing model of vanilla European option and the solving way for pricing the options. Also the model of short interest rate(Vasicek model) are simply introduced.In chapter 3,we study the pricing of quanto options. There are divided into three categories: fixed exchange rate foreign equity call; call on foreign equity denominated in domestic currency; floating exchange rate foreign equity call. And we derive the pricing model and pricing formulas on the assumption that the domestic interest rate follows the Vasicek short-run interest rate model and the exchange rate follows geometric Brownian motion.In chapter 4,the Asian quanto options are discussed. Alao there are divided into three categories: fixed exchange rate foreign equity call with averaged strike;averaged exchange rate foreign equity call; averaged exchange rate foreign equity call with averaged strike. And the corresponding pricing formulas and model are derived.In chapter 5,we discuss the pricing for a class of triggered exchange rate option on the assumption that the domestic interest rate follows the Vasicek short-run interest rate model and the exchange rate follows geometric Brownian motion. And derived the pricing formulas and model. In the final part of this paper,the financial meaning of the solution of the model is also analyzed.