An Assessment of Copula Functions Approach in Conjunction with Factor Model in Portfolio Credit Risk Management

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 systematic risk factors. By coupling with a copula function, e.g., the normal, t-, Clayton, Frank, and Gumbel copula functions, an analytic formulation of the joint distribution of assets’ default times can be derived. On the other hand, 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 the dynamic factor model of Duffee (1999) coupling with a Hawkes process, a class of counting processes allowing intensities to depend on the timing of previous events (Hawkes, 1971) for the contagious effect. Using the factor- contagious-effect model, Monte Carlo simulation is performed to generate default times of two hypothesized firms. It is demonstrated that as the contagious effect increases, the goodness of fit of the joint distribution of assets’ default times based on copula functions decreases, which highlights the deficiency of the copula function approach.