In the new Basel II Accord, banks are allowed to develop their own credit rating models provided that they regularly perform a back test of the risk parameters. However, the lack of sufficient (default) data for back testing rating models for “low-default portfolios ” is a main concern in financial industry and regulators. These low-default portfolios are characterized by the lack of sufficient data and the resulting difficulty in back-testing the Probability of Default. Examples of low-default portfolios are high-quality borrowers, banks, sovereign, insurance companies and some categories of specialized lending. This article presents a method of calibrating low-default portfolios. The method is based on modelling the observed power curve and deriving the calibration from this curve. The functional form of the power curve is determined by a concavity parameter, which can easily be related to the area under the power curve and the Accuracy Ratio (AR). The method is demonstrated for sovereign ratings.

Since the first edition of The Basel Handbook was published in early 2004, major internationally active banks around the world have continued to engage in substantial projects for designing and implementing the extensive Basel II framework. To achieve the

Calibrating low-default portfolios, using the cumulative accuracy profile M. J. van der Burgt ABN AMRO/Group Risk Management/Models and Tools, PO Box 283 (HQ8040),

The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory power. In the second phase of the approach, the raw PD curve is calibrated to fit a target unconditional PD. The concepts and techniques presented include a discussion of different definitions of area under the curve (AUC) and accuracy ratio (AR), a simulation study on the performance of confidence interval estimators for AUC, a discussion of the one-parametric approach to the estimation of PD curves by van der Burgt (2008) and alternative approaches, as well as a simulation study on the performance of the presented PD curve estimators. The topics are treated in depth in order to provide the full rationale behind them and to produce results that can be implemented immediately. 1