A multi-state Vasicek model for correlated default rate and loss severity

Correlation between default and recovery has an important bearing on credit risk capital. Here, Rahul Sen shows that the effect can be modelled efficiently by allowing multiple loss states in the Vasicek framework. Heavy-tailed distributions result for arbitrary loss data, and simple non-parametric capital formulas apply for both large and granular portfolios

The credit component of the Basel economic capital framework is based on Vasicek's portfolio loss model (see Vasicek, 2002, and Schonbucher, 2000). This is a two-state model: at the end of a given period, an obligor is placed in either a non-defaulted state or a defaulted state characterised by a fixed loss severity. Vasicek employs a Gaussian copula framework with a single common factor, the economy, accounting for correlation among obligors. As the economy varies, the portfolio default rate