Portfolio Credit Risk Based on Copulas

Abstract

This paper is devoted to portfolio credit risk based on copulas. The goal of the paper is to combine the portfolio credit risk model and the copula functions to allow better estimation of credit risk by comparing the VaRs at different confidence levels. We will describe the general framework of the portfolio credit risk model, namely threshold models, and Monte Carlo simulation first, then we will provide a basic description of copula functions. In the paper, the CreditMetrics™ model is applied to two well-diversified portfolios consisting of ten bonds traded on the Frank furt Stock Exchange (FSE) from 9 October 2017 to 8 October 2018 to estimate their VaRs at different significance levels. One portfolio is of high quality with ten good-rating bonds, while the other is a credit-risky portfolio with ten risky bonds. After that, CreditMetrics™ with the copula functions is used to recalculate the correlation matrix and the real distribution of the portfolio value. By comparing the VaRs of two different portfolios using both the original CreditMetrics™ model and the CreditMetrics™ model based on the copula functions, we find that the original VaRs of both portfolios are lower than the VaRs calculated based on the copula functions at different con fidence levels, which illustrates that the credit risk is underestimated in the original CreditMetrics™ model for both portfolios. Moreover, the difference between the original VaR and the VaR based on the copula functions is more obvious for the credit-risky portfolio, especially when the confidence level is 95%.