An efficient threshold choice for operational risk capital computation
AbstractOperational 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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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 10096.
Length: 23 pages
Date of creation: Nov 2010
Date of revision: Nov 2011
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Operational risk; generalized Pareto distribution; Picklands estimate; Hill estimate; expectation maximization algorithm; Monte Carlo simulations; VaR.;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-12-18 (All new papers)
- NEP-BAN-2010-12-18 (Banking)
- NEP-CMP-2010-12-18 (Computational Economics)
- NEP-ORE-2010-12-18 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Danielsson, J. & de Haan, L.F.M. & Peng, L. & de Vries, C.G., 2000.
"Using a bootstrap method to choose the sample fraction in tail index estimation,"
Econometric Institute Research Papers
EI 2000-19/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- 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.
- J. Danielsson & L. de Haan & L. Peng & C.G. de Vries, 1997. "Using a Bootstrap Method to choose the Sample Fraction in Tail Index Estimation," Tinbergen Institute Discussion Papers 97-016/4, Tinbergen Institute.
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