基于Tsallis理论的中国股市收益分布研究

应用Tsallis提出的非广延统计力学理论以及与之密切相关的非线性Fokker-Planck方程所描述的动力系统,根据我国上证指数和深证指数2004年1月1日～2008年11月13日的高频数据,分析了在三种不同的时间标度下股指收益的概率分布,发现Tsallis分布可以很好地描述两市收益分布的尖峰厚尾有限方差等特征,同时也给出了市场微观动力学层面的解释。揭示出我国上海和深圳股市的价格过程并不符合随机游走,而是反常扩散过程,两市具有十分接近的非线性动力系统特征。所得结论对于研究我国金融市场的资产配置和定价、风险管理和制度建设都具有重要的意义。

The Research of Returns Distribution of Chinese Stock Market with Tsallis Theory

This paper analyses the probability distribution of stock index returns in three different time scales by using nonextensive statistical mechanics theory 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 suggests that Tsallis distribution can describe the characteristics of fat-tail and finite variance of the two markets,and gives the market microstructure dynamic explanation.It indicates that the stock price processes of Shanghai and Shenzhen markets is 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.