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An efficient threshold choice for operational risk capital computation

Author

Listed:
  • Dominique Guegan

    () (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Hassani

    () (BPCE - BPCE, CES - Centre d'économie de la Sorbonne - UP1 - Université 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00544342, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00544342
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00544342v2
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    References listed on IDEAS

    as
    1. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(02), pages 265-291, November.
    2. repec:hal:journl:halshs-00639666 is not listed on IDEAS
    3. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    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.
    6. Pavel V. Shevchenko & Grigory Temnov, 2009. "Modeling operational risk data reported above a time-varying threshold," Papers 0904.4075, arXiv.org, revised Jul 2009.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dominique Guegan & Bertrand Hassani, 2011. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Documents de travail du Centre d'Economie de la Sorbonne 11017rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2012.
    2. Dominique Guegan & Bertrand Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169268, HAL.
    3. Dominique Guegan & Bertrand K Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Documents de travail du Centre d'Economie de la Sorbonne 15046, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. repec:hal:journl:halshs-00587706 is not listed on IDEAS
    5. repec:hal:journl:halshs-01281940 is not listed on IDEAS
    6. repec:rjr:romjef:v::y:2017:i:3:p:77-87 is not listed on IDEAS
    7. repec:hal:journl:halshs-01169268 is not listed on IDEAS
    8. Dominique Guegan & Bertrand K. Hassani, 2016. "More Accurate Measurement for Enhanced Controls: VaR vs ES?," Documents de travail du Centre d'Economie de la Sorbonne 16015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Dominique Guegan & Bertrand Hassani, 2016. "More Accurate Measurement for Enhanced Controls: VaR vs ES?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01281940, HAL.

    More about this item

    Keywords

    Operational risk; generalized pareto distribution; Picklands estimate; Hill estimate; Expectation Maximization algorithm; VaR; Monte Carlo simulations; méthodes de Monte Carlo; algorithme EM; estimateur de Hill; estimateur de Pickland; distribution de Pareto généralisée; Risques opérationnels;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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