Random Matrix Theory Applied to Correlations in Operational Risk

28 Pages Posted: 30 Mar 2015

See all articles by François Crénin

François Crénin

Société Générale

David Cressey

Société Générale

Sophie Lavaud

Sciences Po - Sciences Po, Students

Jiali Xu

Societe Generale

Pierre Clauss

Société Générale; Université d'Évry - Centre D'Etudes des Politiques Economiques et de L'Emploi (EPEE)

Date Written: March 23, 2015

Abstract

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

Suggested Citation

Crénin, François and Cressey, David and Lavaud, Sophie and Xu, Jiali and Clauss, Pierre, Random Matrix Theory Applied to Correlations in Operational Risk (March 23, 2015). Available at SSRN: https://ssrn.com/abstract=2584992 or http://dx.doi.org/10.2139/ssrn.2584992

François Crénin

Société Générale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

David Cressey

Société Générale ( email )

52 Place de l'Ellipse
La défense, 92000
France

Sophie Lavaud (Contact Author)

Sciences Po - Sciences Po, Students

28 Rue des Saint-Peres
Paris, Paris 75006
France

Jiali Xu

Societe Generale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

Pierre Clauss

Société Générale ( email )

Université d'Évry - Centre D'Etudes des Politiques Economiques et de L'Emploi (EPEE) ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

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