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A Random Matrix Approach on Credit Risk

by Michael C. Münnix of University of Duisburg-Essen,
Rudi Schäfer of University of Duisburg-Essen, and
Thomas Guhr of University of Duisburg-Essen

June 2012

Abstract: We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.

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