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

Abstract

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in 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, the correlations of which 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.

Market states: A new understanding

“…Alternative techniques to handle non-stationary time series through spectral properties have been developed in [3][4][5] . Other approaches to behave at critical or catastrophic moments have been put forward by various authors [6][7][8][9][10] . More recently two of us participated in a proposal 11 to improve the choice of cluster by simultaneously optimizing the clustering process and the noise suppression parameter.…”