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Risks 2018, 6(2), 42;

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

Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
Author to whom correspondence should be addressed.
Received: 28 February 2018 / Revised: 17 April 2018 / Accepted: 19 April 2018 / Published: 23 April 2018
(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)
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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. View Full-Text
Keywords: credit risk; financial markets; non-stationarity; random matrices; structural models; Wishart model credit risk; financial markets; non-stationarity; random matrices; structural models; Wishart model

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Mühlbacher, A.; Guhr, T. Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations. Risks 2018, 6, 42.

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