An assessment of copula functions approach in conjunction with factor model in portfolio credit risk management

Abstract

In credit risk modeling, factor models, either static or dynamic, are often used to account for correlated defaults among a set of financial assets. Within the realm of factor models, default dependence is due to a set of common systemic factors. Conditional on these common factors, defaults are independent. The benefit of a factor model is straightforward coupling with a copula function to give an analytic formulation of the joint distribution of default times. However, factor models fail to account for the contagion mechanism of defaults in which a firm’s default risk increases due to their commercial or financial counterparties’ defaults. This study considers a mixture of the dynamic factor model of Duffee (Review of Financial Studies 12, 197–226, 1999) and a contagious effect in the specification of a Hawkes process, a class of counting processes which allows intensities to depend on the timing of previous events (Hawkes. Biometrika 58(1), 83–90, 1971). Using the mixture factor-contagious-effect model, Monte Carlo simulation is performed to generate default times of two hypothesized firms. The goodness-of-fit of the joint distributions based on the most often used copula functions in literature including the normal, Clayton, Frank, and Gumbel copula, respectively, is assessed against the simulated default times. It is demonstrated that as the contagious effect increases, the goodness of fit of the joint distribution functions based on copula functions decreases, which highlights the deficiency of the copula function approach.​