Loss functions for Loss Given Default model comparison

We propose a new approach for comparing Loss Given Default (LGD) models which is based on loss functions defined 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 differently compared to the traditional approach which only focuses on LGD forecast errors. We apply our methodology to six competing LGD models using a sample of almost 10,000 defaulted credit and leasing contracts provided by an international bank. Our empirical findings clearly show that models' rankings based on capital charge losses differ from those based on the LGD loss functions currently used by regulators, banks, and academics.