The Research Of Returns Distribution Of China's Stock Market Based On Tsallis Theory

This paper analyses the probability distribution of stock index returns in three different time scales by using nonextensive statistical mechanics theory which proposed by Tsallis, closely associated with dynamic system described by the nonlinear Fokker-Planck equations in the financial market modeling, according to the high-frequency data of Shanghai and Shenzhen stock market Index from 2004-1-1 to 2008-11-13,and presents that Tsallis distribution can describe the characteristics of fat-tail and finite variance of the two markets, and gives the market microstructure dynamic explanation. Reveals the stock price processes of Shanghai and Shenzhen markets are not consistent with random walk, but the anomalous diffusion process. The two markets have very similar characteristics of nonlinear dynamic systems. These results for asset allocation and pricing, risk management and institutional development in China's financial markets are of great significance.In this paper, there are several innovations: First, for the first time the nonextension statistical mechanics was applied to the study of Chinese stock markets, explore the changes in stock price formation mechanism and kinetic mechanism; Second, take the stock market as a complex system, use Tsallis distribution to model stock return distribution with high frequency data to verify the Shanghai and Shenzhen stock index; Third, the estimates for the model parameters, taking first obtain the actual return distribution, then the fitting method to improve the accuracy of estimates, avoiding the complicated calculations; fourth, parameter estimates have been based on the returns distribution model, from the perspective of high-frequency trading, well-designed high-frequency trading strategies and risk management strategies, and applied to the stock market and stock index futures markets.