Multivariate Residual Estimation Risk

TL;DR

This paper introduces and extends the concept of residual estimation risk in a multivariate setting, demonstrating its application in credit risk parameter estimation and proposing back-testing methods to evaluate model performance.

Contribution

It provides a practical framework for quantifying residual estimation risk in multivariate models and introduces back-testing criteria for assessing model accuracy and conservatism.

Findings

Residual estimation risk can be effectively quantified using the proposed measures.

Back-testing criteria help evaluate the performance of credit risk models.

Application to retail credit portfolios demonstrates the measure's practical utility.

Abstract

The purpose of this paper is to describe and extend the use of the newly-introduced measure, residual estimation risk. Following the seminal work of Bignozzi and Tsanakas, the quantification of residual estimation risk is proposed in a multivariate framework. Our aim is to provide a succinct and practical introduction to the concept, to motivate its use as a back-testing measure, and to provide examples related to credit risk parameter estimation. In section 2, we introduce residual estimation risk defined by various risk measures, and illustrate the calculation using R and SAS. In section 3, we propose a back-testing criterion for the measure, which can be altered to assess model performance for both accuracy and conservatism. In section 4, we conduct back-testing on risk parameter estimates of retail credit portfolios, including multiple back-testing measures for comparison. Finally, we conclude our findings and propose areas for future work in section 5.