Stock Index VaR Model Under A Stable Distribution And It's Use On Index Future's Deposit

The research in the probability distribution of stock market index return is of great importance to the exploration of the market efficiency, the pricing of financial assets as well as risk management. The traditional theories always assume that the return of financial market follows normal distribution, but in practice it is found that the return of stock index always follows a 'heavy-tailed and skewed' probability distribution, in which traditional normal distribution may not be proper. Because of its better fitness with the 'heavy-tailed and skewed' empirical distribution, stable distribution is now widely used instead of normal distribution. With consideration of China's reality, especially with the coming of index future, the research in the probability distribution of return of Hushen 300 index means a lot in analyzing the velocity of the index return, and what's more, in setting up the proper deposit ratio for the index future. The main contents and results are as follows:1. Introducing related theories and concepts of stable distribution, and also giving out the methods used in calculating the parameters of stable distribution's characteristic function and the probability density function.2. Using both normal distribution and stable distribution to fit the Hushen300 index daily return, and comparing these two results under related statistics tests to draw a conclusion that the return follows stable distribution.3. Introducing related theories and concepts of VaR (Value at Risk), and draw a conclusion through empirical research which is that: no matter under the confidence of 97.5% or 99% the VaR value of stable distribution is greater than that of normal distribution while under the confidence of 95% the VaR value of normal distribution is greater which means that normal distribution tends to underestimate the market risk. And with the result of Kupiec test we find that stable distribution is more able to measure the market risk.4. Giving out a concrete example to show how to calculate the VaR value for both long and short traders under different confidence and different range of period and giving out specified results of the optimistic deposits ratio.