A New Severity Risk Model and Its Application to a Mixed Poisson Credit Risk Model

Abstract

In this article, I develop a generic severity risk model in which LGD is dependent upon PD in an intuitive manner. 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 generic framework, several specifications of stochastic LGD are proposed with detailed calibration method. 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. Applied to a model portfolio, my model behaves as intended and shows the significance of severity risk. Empirical studies suggest that ignoring or incorrectly specifying severity risk can significantly underestimate credit risk, and banks need to consider this in their credit risk modeling and downturn LGD estimation. Associating the severity risk model with other credit risk frameworks such as structural model would be an interesting research topic for the future.