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An efficient threshold choice for operational risk capital computation

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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

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  • Dominique Guegan & Bertrand Hassani & Cédric Naud, 2010. "An efficient threshold choice for operational risk capital computation," Documents de travail du Centre d'Economie de la Sorbonne 10096, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2011.
    • Handle: RePEc:mse:cesdoc:10096
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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. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 265-291, November.
    3. 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.
    4. Dominique Guegan & Bertrand Hassani, 2011. "A mathematical resurgence of risk management: an extreme modeling of expert opinions," Post-Print halshs-00639666, HAL.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    6. 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.
    7. 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.
    8. Pavel V. Shevchenko & Grigory Temnov, 2009. "Modeling operational risk data reported above a time-varying threshold," Papers 0904.4075, arXiv.org, revised Jul 2009.
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    Cited by:

    1. Dominique Guégan & Wayne Tarrant, 2012. "On the necessity of five risk measures," Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
    2. Krzysztof Echaust & Małgorzata Just, 2020. "Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    3. 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.
    4. Dominique Guegan & Bertrand K. Hassani, 2016. "Risk Measures At Risk- Are we missing the point? Discussions around sub-additivity and distortion," Post-Print halshs-01318093, HAL.
    5. Lu Wei & Jianping Li & Xiaoqian Zhu, 2018. "Operational Loss Data Collection: A Literature Review," Annals of Data Science, Springer, vol. 5(3), pages 313-337, September.
    6. Dominique Guegan & Bertrand Hassani, 2012. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Post-Print halshs-00587706, HAL.
    7. Dominique Guegan & Bertrand Hassani, 2016. "More Accurate Measurement for Enhanced Controls: VaR vs ES?," Post-Print halshs-01281940, HAL.
    8. Bertrand K. Hassani & Alexis Renaudin, 2018. "The Cascade Bayesian Approach: Prior Transformation for a Controlled Integration of Internal Data, External Data and Scenarios," Risks, MDPI, vol. 6(2), pages 1-17, April.
    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.
    10. 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.
    11. 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.
    12. Ming-Tao CHUNG & Ming-Hua HSIEH & Yan-Ping CHI, 2017. "Computation of Operational Risk for Financial Institutions," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 77-87, September.
    13. Dominique Guegan & Bertrand Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Post-Print halshs-01169268, HAL.
    14. 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.

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    More about this item

    Keywords

    Operational risk; generalized Pareto distribution; Picklands estimate; Hill estimate; expectation maximization algorithm; Monte Carlo simulations; VaR;
    All these keywords.

    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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