Checking Default Correlation and Score Correlation in a Breakpoint Model for Rating Classification

Abstract In credit risk, debtors with different creditworthiness are divided into rating classes. One problem is to define the borders of the rating classes. A natural way to estimate these breakpoints from default observations comes out of the field of change point analysis. In order to account for dependency between the debtors, the literature proposes a combination of a breakpoint model with a one-factor model. One finds strongly consistent estimators for the threshold of the rating classes and the corresponding default probabilities, also called risk levels. But an investigation of the inherent model properties is as yet missing. For this reason we derive the default correlation and study its relationship to the model parameters, i.e., the breakpoint, the risk levels, and a new correlation term, named score correlation, appearing in a simulation study. Eventually, we check the magnitude of the score correlation used in the simulation study.