Stock Price Follows The Mixing Process Of The Option Pricing Model

This dissertation is intened to study option pricing problems,so as to establish the mathematical model of option pricing with mixed process by means of mathematical tools such as martingale theory and stochastic analysis,to imitate the true trend of stock price,and deduce the option pricing equation.This dessertation is divided into four chapters:Chapter 1 is preface, which introduces the formation mechanism of option value ,and summarizes the sigmificance,origin,development,academic trends.In chapter 2, on the foundation of analytical main impact factor of the option price, suppose the stock price fulfil certain requirement such as Geometric Brownian motion, by making use of arbitrage-free principle and ITO formula,gives the famous Black- Scheoles model and the method how to infer the B-S Model from the B-S Differential Equation. This part elaborate a little on the deduction of B-S partial differential equation, and analyse flaws in the B-S equation.In chapter 3,we make some research about stochastic process that imitate the true trend of stock price,and distinguish feature or characteristic of all kinds of stochastic process.By making a comparison,we analyse rationality, deficiency and defect.In chapter 4, in view of chapter 3,the article make two kinds of new type of modle to simulate stock's changing tendency. The one refers a new mixed process by mixing the Ito process and the Pulse interference process. By changing the basic assumption of Black-Scholes option pricing model, we get European option pricing stochastic differential equation:On the base of the equation,we discuss the European option pricing formula under the condition of paying bonus and failing to pay a dividend.The other one refers a new mixed process by mixing the Ito process and the Markov jump process. By changing the basic assumption of Black-Scholes option pricing model, we get European option pricing stochastic differential equation:On the base of the equation,we discuss the European option pricing formula under the condition of paying bonus and failing to pay a dividend.The two kinds of mixed process not only describe the the underlying assets price fluctuation according to some economic factors,but also give a accurate description about brusque variation. So this modle under the mixed process hypothesis is a better option.