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.
Highlights
IntroductionCredit risk arising from the defaults of their counterparties or borrowers is of great concern
For commercial banks, credit risk arising from the defaults of their counterparties or borrowers is of great concern
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
Summary
Credit risk arising from the defaults of their counterparties or borrowers is of great concern. Considerable popularity among the commercial banks as ways to diversify their exposure to credit risk. A credit default swap (CDS) is the most commonly used tool. Since its introduction in the mid-1990s, the trading volume of CDSs has been growing rapidly. According to Weistroffer, Speyer, and Walter (2009) [1], the peak occurred in 2007 with USD 58 trillion notional amounts outstanding, at over 70% of the debt securities outstanding worldwide at that time
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