Copulas and Credit Risk Models

The topic of this paper is copulas and credit risk models. Generally, there is a core implicit assumption of credit risk models that the critical variables are normally distributed, which is too simplified in the reality. There is no compelling reason for choosing the normal distribution. Therefore, the goal of this paper is to find out the real distributions based on the concept of copulas and then better quantify the credit risk. There is a portfolio that consists of ten bonds issued by quoted companies in the Frankfurt Stock Exchange (FSE) with a 10-million-euro total nominal value over one year, from January 9th, 2017 to January 8th, 2018. The credit risk of the portfolio is quantified under the framework of the CreditMetrics (TM) model, a typical industry example of the threshold models. Two main types of copulas include elliptical copulas and Archimedean copulas. The parameters of a parametric copula are estimated by MLE and then the copula is selected by computing AIC and BIC. Compared with the original CreditMetrics (TM) model with an assumption of normal distribution, the probability density curve obtained based on copulas are more right-tailed and the credit risk of the portfolio is better quantified.