The Option Pricing And Statistics Study Of Random Price Model In Security

In this paper, we are combining percolation theory of the statistical physics and stock market in mathematical finance to study convergence of the limited condition of the stock price. According to poisson distribution and percolation theory, we construct stock price model, and use characteristic function to prove the convergence of this model, we can get that the characteristic function of the constructed model converge on the characteristic function of the Black-Scholes function. Putting jump which is caused by a sudden occurrence into the model for revise, and the new model is more close to the fluctuation of stock price. We furthermore calculate the expectation and variance of random variable, and discuss the approximate value of no-arbitrage price when jump obeying poisson distribution.The security market of our country is a typical complex system, it is affected by some elements, so we need to find a financial model which is more close to the true market, required analyzing some statistics characteristic variable of the security market. We use Ising model to construct security trading volume model constructed, we fit daily trading volume data in Shanghai and Shenzhen exchange of ten securities to statistics characteristic graph, such as accumulate distribution graph, autocorrelation function graph. And the calculated result indicate that the fluctuate of security trading volume in our country has the characteristic of sharp and fat-tails, and the corresponding statistics characteristic graph can reflect law of the truth market.