Loss functions for LGD model comparison Christophe Hurliny, Jérémy Leymariez, Antoine Patinx May 25, 2017 Abstract We propose a new approach for comparing loss given default (LGD) models which is based on loss functions de…ned in terms of regulatory capital charge. Our comparison method improves the banks’ability to absorb their unexpected credit losses, by penalizing more heavily LGD forecast errors made on credits associated with high exposure and long maturity. We also introduce asymmetric loss functions that only penalize the LGD forecast errors that lead to underestimate the regulatory capital. We show theoretically that our approach ranks models di¤erently compared to the traditional approach which only focuses on LGD forecast errors. We apply our methodology to six competing LGD models using a unique sample of almost 10,000 defaulted credit and leasing contracts provided by an international bank. Our empirical …nding clearly show that model rankings based on capital charge losses di¤er drastically from those based on naive LGD loss functions. Keywords: Risk management, Loss Given Default (LGD), Credit Risk Capital Require- ment, Loss Function, Forecasts Comparison JEL classi…cation: G21, G28 . We would like to thank for their comments Denisa Banulescu, Sylvain Benoit, Elena Dumitrescu, Patrick Meidine, Sébastien Michelis, Christophe Pérignon, Samy Taouri-Mouloud, Olivier Scaillet and Sessi Tokpavi. We thank the Chair ACPR/Risk Foundation: Regulation and Systemic Risk, ANR MultiRisk (ANR-16-CE26- 0015-01) for supporting our research. yUniversity of Orléans (LEO, UMRS CNRS 7332). 11 rue de Blois. 45000 FRANCE. Corresponding author:
[email protected] zUniversity of Orléans (LEO, UMRS CNRS 7332).