Random Matrix Theory Applied to Correlations in Operational Risk
28 Pages Posted: 30 Mar 2015
Date Written: March 23, 2015
Measuring correlations among aggregate operational risk losses has a very key impact on calculating regulatory operational risk capital requirement. In the literature, these correlations are often summarized by their average and exhibit a low level. In this paper, we go beyond correlations average and we focus on their distribution. We show that this distribution could present some noise because of the structure of the data of operational risk losses. Consequently, pair-wise correlations estimation and diversification benefits could lack accuracy.
Supervisory guidelines from BCBS for the Avanced Measurement Approaches (AMA) address the issue of the soundness and integrity of the correlation estimates. We propose a sound analysis framework based on Random Matrix Theory (RMT) to control the real levels of observed pair-wise correlations and avoid focusing only on correlations average. We first study the relevant application of this asymptotic theory to small samples. We then determine this improved estimation of observed correlations on a leading operational loss data consortium (ORX). In general, we find strong evidence to reduce the volatility of the correlations distribution that provides sounder correlation estimates.
Keywords: operational risk modeling, correlation and dependence measures, random matrix theory, small samples, ORX database, factor models
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