The art of probability-of-default curve calibration

TL;DR

This paper introduces a new framework for calibrating probability-of-default curves, compares various methods, and demonstrates that the 'scaled likelihood ratio' approach is theoretically sound and empirically superior to the commonly used 'scaled PDs' method.

Contribution

It proposes a comprehensive framework for PD curve calibration and identifies a theoretically justified and more effective alternative to the popular scaled PDs approach.

Findings

The scaled PDs approach is theoretically questionable.

The scaled likelihood ratio approach performs better on datasets.

The framework helps evaluate calibration methods under different conditions.

Abstract

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.