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An efficient threshold choice for operational risk capital computation

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  • Dominique Guegan

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Hassani

    (BPCE - BPCE, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Cédric Naud

    (AON - AON)

Abstract

Operational risk quantification requires dealing with data sets which often present extreme values which have a tremendous impact on capital computations (VaR). In order to take into account these effects we use extreme value distributions to model the tail of the loss distribution function. We focus on the Generalized Pareto Distribution (GPD) and use an extension of the Peak-over-threshold method to estimate the threshold above which the GPD is fitted. This one will be approximated using a Bootstrap method and the EM algorithm is used to estimate the parameters of the distribution fitted below the threshold. We show the impact of the estimation procedure on the computation of the capital requirement - through the VaR - considering other estimation methods used in extreme value theory. Our work points also the importance of the building's choice of the information set by the regulators to compute the capital requirement and we exhibit some incoherence with the actual rules. Particularly, we highlight a problem arising from the granularity which has recently been mentioned by the Basel Committee for Banking Supervision.

Suggested Citation

  • Dominique Guegan & Bertrand Hassani & Cédric Naud, 2010. "An efficient threshold choice for operational risk capital computation," Post-Print halshs-00544342, HAL.
    • Handle: RePEc:hal:journl:halshs-00544342
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00544342v2
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    References listed on IDEAS

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    1. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    2. Luceno, Alberto, 2006. "Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 904-917, November.
    3. Dominique Guegan & Bertrand Hassani, 2011. "A mathematical resurgence of risk management: an extreme modeling of expert opinions," Post-Print halshs-00639666, HAL.
    4. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    5. Dominique Guegan & Bertrand Hassani, 2011. "A mathematical resurgence of risk management: an extreme modeling of expert opinions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639666, HAL.
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