Evaluation of credit portfolio models: test statistics for density-based tests

Credit portfolio model validation is an important area of research that remains neglected. Given that credit defaults are typically rare events, density-based tests as suggested by Berkowitz seem to be the best choice in terms of statistical power Although there are several alternatives, the most commonly chosen test statistic is the likelihood ratio. In this paper we compare its power characteristics with those of three other test statistics. We find that their small-sample characteristics differ remarkably and that the likelihood ratio statistic is not necessarily the best choice. Our results show that the Lagrange multiplier statistic gives more conservative assessments of credit risk, while the Wald statistic tends to underestimate the risks.