Quantification of model risk with an application to probability of default estimation and stress testing for a large corporate portfolio

Michael Jacobs Jr.

Abstract

This paper addresses the building of obligor-level hazard rate corporate probability of default models for stress testing, departing from the predominant practice in wholesale credit modeling of constructing segment-level models for this purpose. We build models based upon varied financial, credit rating, equity market and macroeconomic factors, using an extensive history of large corporate firms sourced from Moody’s.We develop distance-to-default (DTD) risk factors and design hybrid structural/ Merton reduced-form models as challengers to versions of the models containing other individual variables. We measure the model risk attributed to various modeling assumptions according to the principle of relative entropy and observe that the omitted-variable bias with respect to the DTD risk factor, neglect of interaction effects and incorrect link function specification has the greatest, intermediate and least impact, respectively. Given the sensitive regulatory uses of these models and the concerns raised in the industry about the effect of model misspecification on capital and reserves, our conclusion is that validation methods chosen in the stress testing context should be capable of testing model assumptions. Our research adds to the literature in that it offers state-of-the-art techniques as viable options in the arsenal of model validators, developers and supervisors seeking to manage model risk.