Joint Validation of Credit Rating PDs under Default Correlation

The Basel Committee on Banking Supervision recognizes that one of the greatest technical challenges to the implementation of the new Basel II Accord lies on the validation of the banks’ internal credit rating models (CRMs). This study investigates new proposals of statistical tests for validating the PDs (probabilities of default) of CRMs. It distinguishes between proposals aimed at checking calibration and those focused at discriminatory power. The proposed tests recognize the existence of default correlation, deal jointly with the default behaviour of all the ratings and, differently to previous literature, control the error of validating incorrect CRMs. Power sensitivity analysis and strategies for power improvement are discussed, providing insights on the trade-offs and limitations pertained to the calibration tests. An alternative goal is proposed for the tests of discriminatory power and results of power dominance are shown for them with direct practical consequences. Finally, as the proposed tests are asymptotic, Monte-Carlo simulations investigate the small sample bias for varying scenarios of parameters.