Modelling credit grade migration in large portfolios using cumulative t-link transition models

• Heavy-tailed cumulative link models are fit to credit grade transition matrices.
• For a t-link model the degrees of freedom is estimated using maximum likelihood.
• Empirical analysis suggests a t-link with between 1.5 and 4 degrees of freedom.
• The fit is significantly superior to logistic or probit (normal-based) models.
• There is an empirical association between tail-weight and default rate over time.

For a credit portfolio, we are often interested in modelling the migration of accounts between credit grades over time. For a large retail portfolio, data on credit grade migration may be available only in the form of a series of (typically monthly) population transition matrices representing the gross flow of accounts between each pair of credit grades in the given time period. The challenge is to model the transition process on the basis of these aggregate flow matrices. Each row of an observed transition matrix represents a sample from an ordinal probability distribution. Following Malik and Thomas (2012), Feng, Gourieroux, and Jasiak (2008) and McNeil and Wendin (2006), we assume a cumulative link model for these ordinal distributions. Common choices of link function are based on the normal (probit link) or logistic distributions, but the fit to observed data can be poor. In this paper, we investigate the fit of alternative link specifications based on the t-distribution. Such distributions arise naturally when modelling data which arise through aggregating an inhomogeneous sample of obligors, by combining a simple structural-type model for credit migration at the obligor level, with a suitable mixing distribution to model the variability between obligors.