Multivariate Residual Estimation Risk

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.