A Generalized Single Common Factor Model of Portfolio Credit Risk

Abstract

The Vasicek single factor model of portfolio credit loss is generalized to include credits with stochastic exposures (EADs) and loss rates (LGDs). The model can accommodate any distribution and correlation assumptions for the LGDs and EADs and will produce a closedform expression for an asymptotic portfolio's conditional loss rate. Revolving exposures draw against committed lines of credit. Dependence among defaults, EADs, and LGDs are modeled using a single common Gaussian factor. A closed-form expression for an asymptotic portfolio's inverse cumulative conditional loss rate is analyzed for alternative EAD and LGD assumptions. Positive correlation in individual credits' EAD and LGD realizations increases portfolio systematic risk, producing wider ranges and increased skewness in portfolio loss distributions.

Keywords: Credit risk measurement, portfolio credit risk, portfolio loss distribution

JEL Classification: C40, G11, G21, G28