Copula And Nonparametric Kernel Density Estimation

In modern financial analysis, copula study has extremely attractive since it can be used to study the risk management, portfolio aggregation and asset pricing, because the Pearson's linear correlation coefficient is no valid for the most situations in practice. In the paper, we will use Copula, a new technique to measure the dependence between Shanghai and Shenzhen Stock Markets. To search a suitable one, we set up a new method named as Nonparametric Kernel Density Estimation -ML method to get estimators of several copulas. Then through Q-Q test and K-S test, we can compare copulas to get a suitable one. Therefore, we do measure the nonlinear dependent structure among assets conveniently.In this paper, there are two creative points:1) Relaxed the condition on the distribution of assets that involved the problem, because we use the nonparametric density estimation technique.2) Both Q-Q graphic test and K-S test have been used to search a better Copula comparing others, based one the goodness of fitting on given data.The empirical results shows that Gumbel Copula is a better one to descriptive the dependence between Shanghai and Shenzhen stock markets, after compared the several copulas which unknown parameters estimated through the Nonparametric Kernel Density Estimation-ML method.