Stable Distribution Of Stock Index Futures Margin Under Design

The research of financial asset returns has been a long time. The earliest and most classical way in describing the probability distribution of financial asset returns is normal distribution. However, researchers have found through their studies that the empirical distributions of asset returns represent the phenomenon of the heavy tail and excess kurtosis, because of the extreme market moves which seem to occur more frequently than the normal distribution could predict. The traditional distributions usually can not catch these characteristics. The stable distributions allow kurtosis and heavy tails, which can capture the two main characteristic empirical characteristics that heavy-tailed and volatility clustering. Moreover, it can describe the skewness of the data quite well and it has a series of excellent properties.The structure of this paper is as follows:In the preface, we mainly introduce relative backgrounds of research questions in this article and some involved documents at home and abroad. The significance of the research is also indicated.In the chapter 2, after the introduction of related concepts and basic theories of stable distribution, we use both normal distribution and stable distribution to fit the Hushen300 index daily returns and comparing these two results under related statistics tests, including skewness and kurtosis test, Jarque-Bera test and Q-Q plot. we find that the returns refuse the hypothesis of normal distribution obviously. Subsequently, this paper uses R/S method to analyze the fractal feature of Husheng300 stock index. The result also shows the stable distribution is much better than the normal distribution in dealing with stock returns distribution with kurtosis and heavy tails.The basic principles and main computation methods of VaR are introduced in the chapter 3. We compare the strengths and weaknesses among Historical simulation method, Monte Carlo method and Variance-Covariance method, which lay the theoritical foundations for the following sections.In the chapter 4, A new VaR model which is based on the stable distribution is built. Through the empirical research we can draw a conclusion that the VaR model under the stable distribution can measure the risk of stock market much more feasible and effective than the traditional VaR model which is based on the normal distribution. The VaR value of stable distribution is greater than that of normal distribution which means that normal distribution tends to underestimate the market risk, especially under high confidence levels. Further more, We use Kupiec test to verify the accuracy of risk measurement models. And with the result of Kupiec test, we also find that the VaR model based on the stable distribution is able to measure the market risk better.Lastly, in reference to the deposit system of the stock index future market in our country, we design the deposit ratio of Hushen300 index future under the VaR model based on the stable distribution. And then we show how to calculate the VaR value for both long and short traders under different confidence and different range of period through a concrete example, giving out prudent and effective deposit ratio, which can provide some references for investors when they determine the optimistic deposit ratio.The stock index future market is still in its infancy in our country, and the transaction security is of great importance. With consideration of China's reality, especially with the coming of the first Hushen300 stock index future, the research in the probability distribution of return of Hushen300 index means a lot in analyzing the risk value of the index return, and what's more,in setting up the proper deposit ratio for the index future. The purpose of this study is to put forward reasonable and operative methods and techniques to measure the risk of Hushen300 stock index products, which can provide better references for investors and supervisors to weigh, control and manage the risk of the stock market. It is favorable for the safe and efficient operation of futures market in our country, and it can also promote the development and maturity of futures market continuously.