Robust Bernoulli Mixture Models for Credit Portfolio Risk

TL;DR

This paper develops robust Bernoulli mixture models for credit portfolio risk, providing comparison results, risk bounds, and methods to handle model ambiguity, including tail dependencies, with validation through simulations and real data.

Contribution

It introduces a robust framework for Bernoulli mixture models that accounts for model uncertainty and tail dependencies, extending classical credit risk models like CreditMetrics and KMV.

Findings

Provides simple conditions for default probability comparisons

Establishes risk bounds under model ambiguity

Demonstrates effectiveness through simulations and real data

Abstract

This paper presents comparison results and establishes risk bounds for credit portfolios within classes of Bernoulli mixture models, assuming conditionally independent defaults that are stochastically increasing with a common risk factor. We provide simple and interpretable conditions for conditional default probabilities that imply a comparison of credit portfolio losses in convex order. In the case of threshold models, the ranking of portfolio losses is based on a pointwise comparison of the underlying copulas. Our setting includes as special case the well-known Gaussian copula model but allows for general tail dependencies, which are crucial for modeling credit portfolio risks. Moreover, our results extend the classical parameterized models, such as the industry models CreditMetrics and KMV Portfolio Manager, to a robust setting where individual parameters or the copula modeling the dependence structure can be ambiguous. A simulation study and a real data example under model uncertainty offer evidence supporting the effectiveness of our approach.