Joint Default Events and Correlated Migration Moves

Abstract

In the banking industry, the common practice to correlate default and migration events of various guarantors is to use correlated asset price returns. This approach, which is basically a copula approach, is used also by KMV's GCorr model and JPMorgan's CreditMetrics model. However, these models are one-step discrete-time models that are not capable to model joint default events and correlated migration moves for various time horizons in a consistent way, i.e. the forward joint density of default events and migration moves cannot be derived. In this paper we introduce a novel approach to model joint default events and correlated migration moves. After introducing a new definition for describing the dependence structure of processes, we correlate continuous-time Markov chain processes. We show that releasing the Gaussian assumptions and modelling with jumps a new dimension of model uncertainties arises. We introduce various concepts to parameterise the concentration of default events. Furthermore, we extend our models by accounting for the stochastic behaviour of the business time. As part of our comparative analysis, we calculate IRC portfolio loss distributions for various time horizons and hypothetical portfolios and we assess the term structure of default correlations that are implied by the various modelling approaches.