Modeling Portfolio Credit Risk

Abstract

Credit risk constitutes the dominant part of the risks in a portfolio comprising defaultable securities. As a consequence, our ability to model credit risk accurately will play an important role in determining whether the risks in this portfolio can be managed effectively. However, modeling credit risk is a much more difficult task than modeling market risk. Most of the difficulties relate to the differences in the conceptual approaches used for modeling credit risk and data limitations associated with parameter specification and estimation. A particularly difficult parameter to estimate is the credit correlation between two securities because measuring these correlations directly is difficult, if not impossible. Standard techniques used to estimate them follow an indirect approach that makes use of the correlation between variables that drive credit events. For securities issued by corporations, the variable that is usually considered to drive credit events is the asset returns of the firm. Since asset returns are not directly observable, the method used to estimate asset return correlation between different obligors is a much-debated topic. Furthermore, the choice of the joint distribution function for asset returns of different obligors can also have a material impact on the estimate of portfolio credit risk. Keywords: portfolio credit risk; probability of default; recovery rate; rating migration; expected loss; unexpected loss; default correlation; factor model; asset return correlations; transition matrix; migration probabilities; joint credit loss