Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

TL;DR

This paper introduces a random matrix approach to model non-stationary asset correlations in credit risk, effectively capturing tail risks and reducing parameter dependence, with calibration to market data and simulations of joint portfolio risks.

Contribution

It applies random matrix theory to account for non-stationary correlations in credit risk modeling, providing explicit results and improved risk assessment methods.

Findings

Heavy tails dominate diversification benefits even at low correlations.

The random matrix model accurately captures market situations.

Numerical simulations demonstrate joint portfolio risk analysis.

Abstract

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model.