A Study Of Statistical Properties On Stock Price Model By Statistical Physics Theory

In this paper, we apply the contact process to stock markets. Using the contact process, we construct a Stock price model to simulate the return series ofsecurities. The paper contains two parts:In part one, a stock price model is constructed by applying contact process theory. By using a stopping time, we discuss the fluctuations of stock price at the supper-critical state and sub-critical state. At last, we prove that the characteristic function of the stock price convergences to the corresponding characteristic function of the levy process. At last, we simulate the actual data, then prove its rationality.In part two, the data of Shenzhen and Shanghai land indices is analyzed, and the statistical properties of Shenzhen and Shanghai land indices are studied. We select the data for Shenzhen and Shanghai land indices during the year 2001-2006, and investigate the statistical properties by Skewness-Kurtosis test, Kolmogorov—Smirnov test and Hill estimate, we obtain a fat tails phenomena and the power-law distributions of returns for these two land indices. Then we make a comparison of the absolute returns, also give the explanation. At last, we analyze the fluctuation of the relative land prices, and discuss the corresponding probability distributions of the relative land prices.