Probability of default validation: a single-year and a multiyear methodology for the Basel framework

ABSTRACT This paper proposes two methodologies that are designed to test whether observed default rates are in line with default probabilities applied within the Basel framework. This is done by integrating the one-factor model of the Basel framework into the score and the order test statistic. The first methodology, using the score test and a single year of defaults, validates the probability of default assigned to all ratings of a rating system simultaneously. Simulation studies are presented which show that the proposed methodology ensures a type I error that is at the indicated level and is not inflated. The second methodology uses several years' worth of default data and validates the default probability of a single rating by making use of the order statistic. Both methodologies are straightforward to implement and only require rating data.