The Optimal Copula Choice of Index-Related under the Financial Crisis

This article focuses on the dependence of DJI and HIS under the present financial crisis, applying nonparametric kernel density estimation to fit marginal distribution, using maximum likelihood estimation (MLE) to estimate parameters of Copula and adopting different treatments of Kolmogorov-Smirrnov test to choose the best Copula among Archimedes Copulas and Mixed Clayton Copulas. The caulated outcomes show that the Mixed Clayton copula with weight value 0.61 is the optimal Archimedean copula which can illustrate the correlation between DJI and HIS. Moreover, the tail dependence analysis shows that it presents asymmetry, and lower tail's dependence is higher than upper tail's dependence. The fierce fall of DJI's return caused by financial crisis induced fiercer correlated responses on HIS's return, which shows financial crisis's negative influence is tremendous.