Modeling severity risk under PD–LGD correlation

Abstract

In this article, a generic severity risk framework in which loss given default (LGD) is dependent upon probability of default (PD) in an intuitive manner is developed. By modeling the conditional mean of LGD as a function of PD, which also varies with systemic risk factors, this model allows an arbitrary functional relationship between PD and LGD. Based on this framework, several specifications of stochastic LGD are proposed with detailed calibration methods. By combining these models with an extension of CreditRisk+, a versatile mixed Poisson credit risk model that is capable of handling both risk factor correlation and PD–LGD dependency is developed. An efficient simulation algorithm based on importance sampling is also introduced for risk calculation. Empirical studies suggest that ignoring or incorrectly specifying severity risk can significantly underestimate credit risk and a properly defined severity risk model is critical for credit risk measurement as well as downturn LGD estimation.