Max-factor individual risk models with application to credit portfolios

TL;DR

This paper introduces max-factor models for individual risk in credit portfolios, replacing linear combinations with maxima to better identify dominant factors and improve dependence modeling.

Contribution

The paper proposes a novel max-factor approach for dependence modeling in credit risk, addressing limitations of linear combinations in capturing dominant factors.

Findings

Max-factor models provide clearer identification of dominant risk factors.

The approach improves the modeling of joint default probabilities.

Enhanced understanding of dependence structures in credit portfolios.

Abstract

Individual risk models need to capture possible correlations as failing to do so typically results in an underestimation of extreme quantiles of the aggregate loss. Such dependence modelling is particularly important for managing credit risk, for instance, where joint defaults are a major cause of concern. Often, the dependence between the individual loss occurrence indicators is driven by a small number of unobservable factors. Conditional loss probabilities are then expressed as monotone functions of linear combinations of these hidden factors. However, combining the factors in a linear way allows for some compensation between them. Such diversification effects are not always desirable and this is why the present work proposes a new model replacing linear combinations with maxima. These max-factor models give more insight into which of the factors is dominant.