Stochastic Percolation Stock Price Modeling And Option Price Research

It is believed in traditional theory that in a certain stock market,the stock price process and the return process of stock index are similar to Gaussian Distribution. However,the study in the recent years has shown that the distribution of returm of financial time series nearly obeys central Levy distribution and it has shown the"fat tail phenomenon.In this paper,we have applied the percolation theory of statistical physics in the stock market to study,simulate and analyze the stock price process,we also have studied the corresponding European option pricing problem.We consider a stock price model that contains two groups of investors:Group A and Group B.Investors in Group A are seen as chartists who are very rational and make the investments according to the analysis of historical data and investment strategies.Their investment behaviors will make the fluctuation of stock price obey Black-Scholes formula Kt=(?)uA(t)dt+(?)σ(t)db(t); Investors m Group B are seen as detailers, they get news through a long-range percolation model and they completely follow the trend in the market to invest,this will cause huge fluctuation for the stock price.Under the influence of these investors,there will be a jump component in the stock price model which obeys Compound Poisson Process:(?)t=(?)hiμ.In the study of the option pricing problem,we will show one reasonable arbitrage-free European option pricing formula according to the stock price model with jump component which obeys Compound Poisson Process that we have gained.