Study On Application Of Stochastic Processes Theory For Pricing Option

In this paper, we will use the stochastic processes theory such as Markov chains, Poisson process , stopping time to construct different models describing the waviness of stock. Considering the influence of stock trading volume, we discuss how to price a European call option and avoid risk.It is a branch of Mathematical Finance to study the fluctuations of stock prices in a stock market. Because of the instability of financial phenomenon, the stochastic processes theory as an important part of probability is applied to do a research of the financial problems. The second part and third part in this paper describes the fluctuations of stock prices respectively on the base of Poisson process and stopping time. At the beginning of each part we introduce some basic knowledge of financial mathematics. For example: Poisson process, compound Poisson process, Markov chains, European option, stopping time and so on.On the base of Markov chains theory we bring stock trading volume to a model describing the waviness of stock price. With the knowledge of Poisson process and stopping time , different model is constructed in Part 2 and Part 3. According to the theory of pricing option as well as the models, we obtain the formula for pricing a European call option. In respect that investors always put avoiding and controlling risk primacy in their financial investment, it is very important to set up and study the corresponding theory and means about investment for investors. Moreover we give the range of European call option price in a risk-averse market in this paper.