(Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution

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(Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution

by Christian Gourieroux of CREST, CEPREMAP & the University of Toronto, and
Alain Monfort of CNAM & CREST

December 2006

Abstract: In this paper, we explain why a nonparametric approach based on a beta kernel [Renault, Scaillet (2004)] will lead to significant bias when applied to recovery rate distributions. This is due to a specific feature of these distributions, which admit strictly positive weights at 100% corresponding to full recovery (and also at 0% corresponding to total loss). Moreover, for distributions without point mass at 0% and 100%, the beta kernel approach features significant bias in finite sample. In large sample, the method is consistent, but other competing approaches presented in the paper provide more accurate results.

JEL Classification: C13, C14, G33.

Keywords: Loss-Given-Default, Recovery, Credit Risk, Kernel Estimation.

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