A Study On Stock Index Futures Hedging Based On Geometric Spectral Risk

On April16,2010, the first launch of stock index futures providing the investors a effective tool to hedge systemic risk. Investors can take advantage of the stock index futures to conduct hedging operations to achieve the purpose of avoiding risk, among them, the core issue of hedging is the determination of the hedging ratio, which is the main purpose of this paper. In this paper, the purpose of our research is minimum the risk of the hedge ratio based on the framework of minimum risk, and the optimal hedging ratio is obtained by optimization calculation.This paper revolves three issuess, first of all, which tool is the best to measure risk; Secondly, which method is the best to calculate the optimal hedging ratio; Finally, which kind of evaluation is suitable to compare different advantages and disadvantages of the model.This article analyzes the variance (standard deviation), value at risk (VaR), conditional value at risk (CVaR), the expected loss (ES) and the geometric nature of the risk spectrum (GM) in detail. The result of comparing is that geometric spectral risk is the most scientific as a risk measure. So in this article, risk hedging portfolio was measured by GM to establish the objective function, then we using a nonparametric method to determine geometric spectral minimum risk under the constraint of the optimal hedging ratio. The advantage of nonparametric method is that it does not need to assume any distribution of the asset return, it will not disturbed by the errors of model specification, and it can better revert the information and internal laws that contained by the data. The detailed operating method is to find the hedging ratio that matched with the minimum geometric risk of the hedging portfolios by grid search method, this kind of hedging ratio is the desired hedge ratio is in this paper. The index of the performance evaluation is the change of skewness and kurtosis, the change of the geometry spectrum risk, and the change of standard deviation. To overcoming the shortcomings of the historical simulation method, this paper uses copula function to improve the calculations of the hedging ratio. Copula can well capture the construction of the nonlinear correlation between assets structure, and it can well measure the asymmetric correlation, which overcomes the challenge of the nonlinear price linkage pattern of the linear kernel hedging model. Chapter7illustrate the application process of copula in detail, and shows the flow chart of model. First of all, according to the sampling data of spot and futures returns, this article uses the gauss kernel function and kernel density estimation method to estimate yield density function, then cumulating the density function to obtain cumulative distribution function of the spot and futures returns, choosing the best distribution of copulas function to fit spot and futures joint distributions. The empirical results show that Clayton copula connect function is able to capture the correlation structure of spot and futures ideally. According to the joint distribution, we use Monte Carlo simulation and the grid search method to obtain the optimal hedging ratio under the minimum in GM constraints, copulas connect method can get the large sample size of the spot and futures. Without extending the time of returning back, in order to improve the estimation precision of the model, at the same time doesn’t change the related structures between assets.We collect the day’s closing price of the CSI300index and the CSI300stock index futures from April16,2010to July12,2012.Then we use logarithm of the yield data. We conduct the empirical research by using out of sample data and in the sample data. For in the sample research, we use the static hedging strategy, for out of the sample research, we adopts a dynamic strategy of moving window. Contrast model is the least squares estimate method (OLS), Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, the minimum value at risk (VaR) model and the minimum condition value at risk (CVaR) model.The empirical results show that the hedging ratio of geometric spectral risk is the minimum value compared to the other four models, regardless of the data form. At the same time, the amount of change of skewness, kurtosis and the geometric spectral risk of hedging ratio is also better than other several models. The portfolio of geometric spectral risk shows the biggest change of skewness, the minimum kurtosis added value, and the highest GM reducing degree. Specially, only in the standard deviation, the reducing degree of geometric spectral risk is not the biggest. On the whole, the performance of the minimum optimal geometric spectral risk model is the best, not only it can effectively reduce the risk, but also it can save the cost of hedging.This paper combined nonparametric methods and copula connect function to study the hedging of China’s stock index futures. We hope that it can give investors some reference for hedging.