A Markovian infectious model for dependent default risk

Abstract

Modelling dependent defaults has long been a central issue for credit risk measurement and management. To address this important issue, we introduce a Markovian infectious model to describe the dependent relationship of default processes of credit securities. The central tenant of the proposed model is the concept of common shocks which is one of the major approaches to describe insurance risk. Using real data default data, we compare the proposed model to some existing default risk models, such as one-sector and two-sector models discussed in Ching et al. (2008, 2010). A log likelihood ratio test is adopted for the purpose of model comparison. Our empirical results reveal that the proposed model outperforms both the one-sector and two-sector models. We also illustrate the application of the proposed model for quantitative risk measurement. In particular, numerical results for both the crisis value-at-risk and the crisis expected shortfall are provided.