Credit risk - A structural model with jumps and correlations

TL;DR

This paper introduces a comprehensive structural credit risk model incorporating jumps and correlations among multiple companies, analyzed both analytically and through extensive simulations to understand loss distributions and risk measures.

Contribution

It develops a novel jump-diffusion structural model for credit risk that includes correlations and provides both analytical insights and detailed numerical analysis.

Findings

Loss distribution and moments depend strongly on model parameters

Correlations significantly influence portfolio risk measures

Analytical solutions are feasible for simplified model versions

Abstract

We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations between the companies. We discuss that models of this type have much in common with other problems in statistical physics and in the theory of complex systems. We study a simplified version of our model analytically. Furthermore, we perform extensive numerical simulations for the full model. The observables are the loss distribution of the credit portfolio, its moments and other quantities derived thereof. We compile detailed information about the parameter dependence of these observables. In the course of setting up and analyzing our model, we also give a review of credit risk modeling for a physics audience.