Heterogeneous credit portfolios and the dynamics of the aggregate losses

TL;DR

This paper introduces a tractable intensity-based model for heterogeneous credit portfolios that accounts for firm-specific characteristics and contagion effects, enabling quantitative analysis of large portfolio losses.

Contribution

It develops a novel heterogeneity-aware model with a large deviation framework, extending traditional homogeneous models for more realistic credit risk assessment.

Findings

Model captures firm heterogeneity and contagion effects.

Law of large numbers and central limit theorem derived for portfolio losses.

Simulation results demonstrate model's applicability to loss distribution analysis.

Abstract

We study the impact of contagion in a network of firms facing credit risk. We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large number and a central limit theorem useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.