Journal of Operational Risk

Random matrix theory applied to correlations in operational risk

Pierre Clauss, Jiali Xu, Sophie Lavaud, David Cressey and François Crénin

  • This paper proposes to apply Random Matrix Theory to calibrate operational risk correlations, which has never been done before.
  • The possibility of such theory to work in small dimension is shown.
  • Cleaning method to get a sound correlation matrix is proposed.


Measuring correlations among aggregate operational risk losses has a significant impact on calculating regulatory operational risk capital requirements. In the literature, these correlations are often summarized by their average and exhibit a low level. In this paper, we go beyond the average of correlations 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, pairwise correlations estimation and diversification benefits could lack accuracy. Supervisory guidelines from the Basel Committee for Banking Supervision for the advanced measurement approach address the issue of the soundness and integrity of the correlation estimates. We propose a sound analysis framework based on random matrix theory to control the real levels of observed pairwise 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. In general, we find strong evidence to reduce the volatility of the correlations distribution that provides sounder correlation estimates.

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