The Study On Measuring Default Correlation With Copula Approach

Copula approach is a powerful tool to study dependence structure of multiple random variables. Using this approach, we can consider marginal distribution from the joint distribution separately and can choose marginal distribution flexibly. Different copula function represents different dependence structure. Using copula approach to analyze joint default, we can describe credit portfolio structure more accurately, especially the tail dependence level. In this paper, we analyze default correlation based on the linear correlation coefficient, and focus on the difference of the tail probability of losses distribution between Gaussian copula and t-copula. Moreover we discuss the application of Archimedes copula, Marshall-Olkin copula in joint default.A major problem of copula approach in the practical application is how to choose a copula function. In this paper, we test the fit of the tail dependence structure of the given data among several copula functions by using two different goodness of fit test method, and receive a good result. On fat tail structure of the given data, the law of A-D goodness of fit test is better than the K-S goodness of fit test, the former is more sensitive and rational.