Modeling Intra and Inter Correlations in Credit Default Losses

Abstract

Comparing alternatives for a simultaneous incorporation of intra and inter correlations into the credit portfolio loss distribution within the asymptotic single risk factor (ASRF) model and showing that the resulting distribution depends on the type of a dominant correlation: whether it is of intra d-d/lgd-lgd or inter d-lgd type. Showing that the classic Vasicek distribution (derived originally for intra d-d correlations only), modified to embrace both intra and inter correlation types by properly constructing composite mean and correlation parameters, offers an analytic solution which covers an entire range of correlations and is easy to use as opposed to a more formal approach of a bivariate joint default probability density which requires numerical averaging over the underlying latent factors and applies only when intra correlations dominate.