Application of Copula-GARCH to Estimate VaR of a Portfolio with Credit Default Swaps

Abstract

Credit Default Swaps (CDSs) provide an efficient way for commercial banks to hedge their portfolios’ exposure to credit risk. Following Patton (2006), Huang, Lee, Liang, and Lin (2009), and Fei, Fuertes, and Kalotychou (2013), we proposed a way to estimate Value-at-Risk (VaR) of portfolios containing CDSs that is better than the traditional methods mentioned in financial textbooks. Markit’s North American Investment Grade CDX Index (CDX.NA.IG) is a combination index of 125 North American entities with investment-grade credit ratings that trade in the CDS market. Each of the S & P 500 index and VIX are used with CDX.NA.IG to construct portfolios. This paper uses 2,477 daily data items from December 2004 to October 2014 covering the period of the subprime mortgage crisis and the European debt crisis. We chose six constant and two time-varying copula models combined with GARCH skewed Student-t innovation (GARCH-skt) to form eight copula-GARCH models to capture the joint distribution of the two assets in the portfolio. We then computed corresponding 1-day VaRs. According to our findings, the time-varying symmetrized Joe-Clayton (SJC) copula model combined with the GARCH-skt (tvSJC-copula–GARCH-skt) performed best, regardless of the market situation. Not surprisingly, this result stems mainly from this model’s consideration of the serial correlation in the individual index return and the time-varying nonlinear dependency between indices.