PD curve calibration refers to the transformation of a set of rating grade-level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration approaches and the conditions under which they are fit for purpose. We test the approaches discussed by applying them to a publicly available dataset of agency rating and default statistics that can be considered typical for the scope of application of the approaches. We show that the popular 'scaled PD curve ' approach is theoretically questionable and does not perform well on the test datasets. We identify two calibration approaches that are both theoretically sound and perform much better on the test datasets. Keywords: Probability of default, calibration, likelihood ratio, Bayes' formula, rating profile, binary classification.
PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration approaches and the conditions under which they are fit for purpose. We test the approaches discussed by applying them to publicly available datasets of agency rating and default statistics that can be considered typical for the scope of application of the approaches. We show that the popular 'scaled PDs ' approach is theoretically questionable and identify an alternative calibration approach ('scaled likelihood ratio') that is both theoretically sound and performs better on the test datasets. Keywords: Probability of default, calibration, likelihood ratio, Bayes' formula, rating profile, binary classification.
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