Research On VaR Of Chinese Stock Market Based On Stable Distribution

Right investment decision requires reliable predictions of return and risk, and reliable predictions can only be obtained if the underlying statistical model tests on realistic assumptions. The traditional portfolio theory is based on the normal distribution for the real distribution of stock market in China. But the real distribution of financial data follows a heavy-tailed and skewed distribution. Stable laws are able to capture the two main characteristic of empirical evidence. The stable distribution of the stock returns of Shenzhen stock market and Shanghai stock market are discussed and the VaR under the stable distribution is further researched. The main contents and results are as follows:1. The basic theories of univariate stable distribution and multivariate stable distributions and stable stochastic processes are introduced.2. The selected stock returns in the stock market are analyzed by the means of the normal distribution and stable distribution simulation. For every type of selected distribution simulation optimistic are measured by the maximum likely parameter estimation and x2 test Contrasting all the results of function, the lowest simulation option is the best distribution. The results show the stable distribution is much better than the normal distribution in dealing with stock returns distribution with fat tail.3. The basic principle and main methods of VaR computation are researched. The analytical method, history simulation method and Monte Carlo Simulation are contrasted.4. Value at Risk under the stable distribution are researched in the Chinese stock market. One of the important questions is the validity of the model. Because VaR under the stable distribution are statistical and prediction model based on the history data or the presumed statistical parameter and distribution, whether it can predict the risk correctly or not must be tested. The main method is back testing. Applying this statistical model to VaR test, the real profit and loss data of financial asset is contrasted to the prediction in a period to test the validity of VaR. Through the backing test of Shanghai and Shenzhen stock market under the three model of analytical method, historical simulation method and stable distribution, the result shows the VaR model can measure the risk of stock market in China.