Probability of Default Validation : Introducing the Likelihood-Ratio Test and Power Considerations

The aim of validating default probabilities is to analyze whether these are not too low. For small sample sizes, however, there are not enough observations available to detect excessively low default probabilities.We therefore propose a modification of default probability validation which ensures that default probabilities that are too low are rejected with a certain minimum probability. Also, we introduce the likelihood-ratio test applied to the likelihood function derived from the one-factor model and suggest its usage for default probability validation, instead of a test that assumes independent observations