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Correlation Risk
Modeling and Management

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Correlation Risk
Modeling and Management

An Applied Guide Including the
Basel III Correlation Framework— with Interactive Correlation Models

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

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Mathematical Analysis in Investment Theory

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AN INTRODUCTION to ECONOPHYSICS Correlations and Complexity in Finance

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Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations Andreas Mühlbacher∗ and Thomas Guhr Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany March 2, 2018 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. 1 Introduction To assess the impact of credit risk on the systemic stability of the financial markets and the economy as a whole is of considerable importance as the subprime crisis of 2007-2009 arXiv:1803.00261v1 [q-fin.RM] 1 Mar 2018 and the events following the collapse of Lehman Brothers drastically demonstrated [24].
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Albanese, C., 285 Altman E., 61 Andersen, L., 134 Anderson, M., 65

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Copula Models and the Financial Crisis: How to Price Synthetic Cdos’ Tranches

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