Affine models for credit risk analysis

Continuous-time affine models have been recently introduced in the theoretical financial literature on credit risk. They provide a coherent modeling, rather easy to implement, but have not yet encountered the expected success among practitioners and regulators. This is likely due to a lack of flexibility of these models, which often implied poor fit, especially compared to more ad hoc approaches proposed by the industry. The aim of this article is to explain that this lack of flexibility is mainly due to the continuous-time assumption. We develop a discrete-time affine analysis of credit risk, explain how different types of factors can be introduced to capture separately the term structure of default correlation, default heterogeneity, correlation between default, and loss-given-default; we also explain why the factor dynamics are less constrained in discrete time and are able to reproduce complicated cycle effects. These models are finally used to derive a credit-VaR and various decompositions of the spreads for corporate bonds or first-to-default basket.