Option Pricing Modol When Stock Pricing Process Is A Jump-Diffusion Process

Effective management of risk occupies the right evaluation of derivative securities.The critical thing that the financial derivative securities exist reasonably and develop properly is how to value its fair price.Among all the pricing systems,the investigation of option pricing is most extensive.The reasons for this are:Compared to other derivative securities,option is easy to price;many derivative securities appear in the form of optionjthe pricing principles are same to all sorts of derivative securities,so it is possible to find pricing theory of common derivative securities through the option pricing methods.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.This dissertation is intended to study option pricing problems,so as to establish the mathe-matic r- 'dule of option pricing with jump-diffusion process by means of mathematical tools such as martingale theory and stochastic analysis, to deduce the option pricing equation .This dessertation is divided into four chapters:Chapter 1 is preface,which summarizes the sigmificance,origin,development,academic trends.In chapter 2,we introduce the models of stock price submitting to the exponential Ornstein-Uhlenbeck process and Black-Scholes option pricing ,and we found that they are equal under the equivalent martingale probability measures P* and PL equivalent to P.Under the two models their stock price have the same stochastic differential equation:so the price of options are equal.In chapter 3,the variation in price of stock not only has a contiuous of time ,but also has brusque variation( release of an unexpected economic figure.major political changes or natural disaster) .we call the discontinuous function of time "jump" .under the hypothesis of stock price submitting to jump-diffusion process model,we gets its option pricing formula by use of the martingale approachand the jump process is renewal process.In chapter 4,considering dividend.we establish the option pricing model with jump-diffusion process. Under the hypothesis of continuous dividend, if the continuous dividend rate is p ,then the price of stock St submit to the stochastic differential equation: we get European call and put option pricing formula and their parity.