Tsallis Statistical Distribution And Its Application In The Risk Estimation Of Financial Market

The random phenomena in the natural world is complex. How to identify the hidden law by analyzing is the goal which is pursued by people people for many years. From a statistical point of view, the distribution function has made a huge success in describing that. However, with the deepening of the study, relying on the existing distribution has been unable to meet the needs of the research. So, to find out new forms of statistical distribution is essential for scientific research in future.The maximum entropy principle is an important principle of entropy theory. It is the bridge of the entropy and the statistical distribution linked together very well. In order to making up for the lack of the existing statistical distribution in descriping random phenomena of the nature, using the maximum entropy principle, on the basis of entropy theory, derive series of entropy statistical distribution. The statistical distribution launched by Boltzmann-Gibbs entropy is called the BG statistical distribution, that is the "classic" statistical distribution; The statistical distribution launched by Tsallis entropy is called Tsallis statistical distribution, that is the "extended" statistical distribution or q-distribution. Tsallis statistical distribution is a promotion of the BG statistical distribution, It has a dynamic parameter, when q→1, Tsallis statistical distribution is the BG statistical distribution.Today, the financial system is more and more international and Market-oriented, the stock market volatility is increasing and the risk was significantly increased, so the distribution patterns of the capital gains rate is more complicated. Many studies have shown that the distribution of stock returns has a heavy tail characteristics, such problems is difficult to describe with a normal distribution.In order to verify the application value of Tsallis statistical distribution, Canada S&P-TSX60index is selected for the sample data. First, to analysis the basic statistical properties of the sample data with spss; Second, to determine that the sample data is non-normal and thick tail with JB test method and the QQ plot;Then, to calculate the VaR of the financial marke by the Tsallis statistical dynamic structure model. Tsallis-q-Gauss distribution in the calculation of VaR, emphasis on the tail risk usually ignored by variance covariance method. The VaR value calculated by the Tsallis-q-Gauss distribution and the VaR values calculated by the normal distribution satisfy a Linear relationship. We can calculate the VaR value under the Tsallis-q-Gauss distribution through the VaR values calculated by the normal distribution.