The Empirical Research On The Risk And Hedging Ratio Of China Stock Index Futures Based On Copula Function

April 16,2010, china stock index futures turns out, and it opens a new chapter in the domestic capital market. Stock index futures is a risk management tools, and because of the leverage of margin trading, the risk is magnified. So risk measurement of the portfolio including stock index futures is very important. On the mean time, the stock index futures can not only distribute and transfer investors' financial risk effectively as a risk management tool, but also have the functions of hedging which can earn profits for investors. Stock index futures in China has launched nearly a year's time. More and more investors and institutions involved in stock index futures market, the capital market is waiting for a comprehensive study of stock index futures and spot for a long time. Therefore, at this stage a comprehensive review of the dynamic hedging rate and the risk characteristics of the china stock index futures has a certain academic value and practical significance.Based on this, the two questions this article focued on are:(1) Risk measurement of the stock index futures and portfolio including stock index futures. In this paper, we use Copula functions to discuss the non-linear dependency model of china stock index futures and Skew-t distribution for the marginal distribution. Then application of MC simulation technique, we calculate the portfolio VaR values in two case of holding long and short stock index futures. We also calculated the optimal investment ratio. This provide a reliable basis for investors in risk management.(2) Calculation of optimal dynamic hedging rate, based on time-varying Copula model. In the minimum variance principle, we systematically studied the stock index futures optimal dynamic hedging rate and efficiency of the evaluation.We use normal Copula function and t-Copula function to estimate the non-linear correlation coefficient. We also construct a weighted nonlinear correlation coefficient using normal Copula function and the SJC-Copula function Copula to calculate the optimal hedge ratio. Compared with the traditional OLS model and BEKK model, the empirical results show that the hedging effectiveness of the model based on Copula functions is significantly higher than the traditional model. The main conclusions of this paper is as follows:(1) The yields of stock index futures is largely consistent with movement in the yields of spot, with a high correlation between them. This shows that investors can use index futures to hedge.(2) The estimation results show that there are a high tail correlation between stock index futures and spot. There are non-symmetrical tail dependencies, and the up tail correlation coefficient is greater than low tail correlation. We calculate the portfolio VaR values in two case of holding long and short stock index futures. By changing the investment ratio,we can find the optimal portfolio based on minimizing risk. This provide a reliable basis for investors in asset allocation.(3) In this paper, the hedging effects of five Copula-GJR model are superior to the traditional OLS model and the BEKK model, and the weighted coefficient of this model constructed is best. In short, we can see the dynamic Copula model is quite successful in hedge research.The empirical study of this paper come to a good conclusion, but there are many inadequacies.(1) Due to sample size limitations, this paper does not carry out post-test, but gives the calculation and results, based on the dynamic SJC-Copula model in the calculation of portfolio VaR.(2) In order to simplify the hedge research, the transaction costs in this paper is ignored. This makes the model in the specific operation has certain limitations.(3) In this paper, we only consider the time-varying Copula model, assuming the form of Copula functions do not change over time. However, if the basic form of Copula function changes over time, the practical application of the model will be greatly reduced.There are two innovations in this article:(1) In this paper, we use dynamic SJC-Copula function to measure relevance of stock index futures and spot. We calculate the portfolio VaR values and the optimal investment ratio in two case of holding long and short stock index futures.(2) We systematically studied the stock index futures optimal dynamic hedging rate and efficiency of the evaluation. We also construct a weighted nonlinear correlation coefficient to calculate the optimal hedge ratio, using the normal Copula function and SJC-Copula function Copula. The empirical results show that this model has the advantage of exiting hedge ratios models.