The Art of PD Curve Calibration

by Dirk Tasche of Financial Services Authority, UK

January 24, 2013

Abstract: PD curve calibration refers to the task of transforming a set of conditional probabilities of default (PDs) to another average PD level that is determined by a change of the underlying unconditional PD. This paper presents a framework that allows to explore a variety of calibration techniques and the conditions under which they are fit for purpose. We test the techniques 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 techniques. We show that the popular technique of 'scaling the PD curve' is theoretically questionable and does not perform well on the test datasets. We identify two calibration techniques that are both theoretically sound and perform much better on the test datasets.

JEL Classification: C13, G24.

AMS Classification: 62F10, 91B70.

Keywords: Probability of default, calibration, likelihood ratio, Bayes' formula, rating profile.

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