Copula界在多元VaR中的应用

Application of Copula Bound in Multivariate VaR

首先介绍了多元随机变量和的边界,以及由此导出的VaR边界,然后全面总结了有关Copula下界的公式,而Copula下界及其对偶函数分别构成计算VaR边界的依据.最后根据VaR边界的数值算法,针对不同的Copula下界,分多种情景详细分析了VaR的边界范围.关于上证指数和深成指数收益率序列的实证分析发现.Spearman相关系数和正象限相依对VaR界的收窄作用最强.

First, we illustrate the bounds of random variables sum and VaR bounds. Second, we summarize the low bounds of Copula, which are used to deduce VaR bounds. Finally, we introduce the numerical method for calculating VaR bounds, and analyze different VaR bounds with lots of scenarios for different low bounds of Copula. Appling the theory of VaR bounds to the return series of Shanghai Composite Index and Shenzhen Component Index, we find that Spearman correlation and positive quadrant dependence are better than other dependence information for narrowing the bounds of VaR.