The Application Of Copulas To Credit Risk Management

The joint distribution of random variables fully incorporates the information of margins and dependent structure. But when analyzing high dimensional joint distribution, it is necessary to separate margins and dependent structure for the purpose of simplicity. A copula function of a joint distribution is a function that describes how and to what extent do random variables dependent on each other without considering their marginal distributions. This attractive property makes it possible for us to employ copula to do research on the joint occurrence of risk events.When get a closer look at the four popular credit risk models as CreditMetrics KMV CreditRisk+ and CreditPortfolio View, it is very clear that the mathematical essentials of each model lie in the way the joint distribution of the so-called 'default indicators' is modeled, a vector of Bernoulli random variables. In a common way, normal distribution is selected. But as it was shown in most financial articles normal copula is not proper for the real world. This article proposes to use t-copula, Marshall-Olkin copula and Achimedean copula to revise these models. The conclusion is that using new copulas instead of normal copula, the tails of loss distributions will be heavier and scattered.