Conditional and Dependent Credit Migrations in a Factor Model Copula Framework

We review different methods for simulating credit migrations in a nonparametric and discrete or continuous-time Markov chain framework. We suggest the application of a factor model approach in combination with the use of copulas for the joint dynamics of credit rating changes. While there are several applications of copulas in credit risk for modeling joint defaults, it lacks of the same interest towards modeling dependence in rating migrations. It is well-known, however, that the risk of a credit portfolio is not dependent only on the defaults but also on rating upgrades and downgrades. In a simulation study, we illustrate the effects of considering dependencies in credit migrations for an exemplary loan portfolio. Hereby, we do not only examine default or loss figures for the portfolio, but also the distribution of ratings by the end of the simulated period. Our findings illustrate quite large differences between the different approaches: not only the fact whether dependence is accounted for but also the choice of the copula affects loss figures and the distribution of ratings. Also extreme outcomes for credit migrations like they have been observed during times of a financial crisis can be modeled introducing an adequate level of dependence. The approach may be in particular helpful for scenario analysis and stress testing in credit risk management.