Assessing the discriminatory power of loss given default models

Abstract

For banks using the Advanced Internal Ratings-Based Approach in accordance with Basel III requirements, the amount of required regulatory capital relies on the banks' estimates of the probability of default, the loss given default and the conversion factor for their credit risk portfolio. Therefore, for both model development and validation, assessing the models' predictive and discriminatory abilities is of key importance in order to ensure an adequate quantification of risk. This paper compares different measures of discriminatory power suitable for multi-class target variables such as in loss given default (LGD) models, which are currently used among banks and supervisory authorities. This analysis highlights the disadvantages of using measures that solely rely on pairwise comparisons when applied in a multi-class setting. Thus, for multi-class classification problems, we suggest using a generalisation of the well-known area under the receiver operating characteristic (ROC) curve known as the volume under the ROC surface (VUS). Furthermore, we present the R-package VUROCS, which allows for a time-efficient computation of the VUS as well as associated (co)variance estimates and illustrate its usage based on real-world loss data and validation principles.

Keywords:

• Loss given default
• volume under surface
• discriminatory power
• receiver operating characteristic

2010 Mathematics Subject Classification:

• 62P05

Acknowledgments

The authors are grateful to Manveer Mangat who supported coding and drafting in early stages of the project. The paper expresses the authors' views and does not represent official positions of the Oesterreichische Nationalbank.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Simulations with $k=2,6,10,\dots ,58$ classes and $n=100,123,146,\dots ,1000$ observations indicate that the implementations of Somers' D result in an average decrease in computation time of around $96\mathrm{\%}$ (measured using R's microbenchmark package with 1000 repetitions) compared to the implementation found in R's DescTools package (Version 0.99.24).