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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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
Contact details of provider:
Postal: 106-112 boulevard de l'Hôpital 75 647 PARIS CEDEX 13
Phone: + 33 44 07 81 00
Fax: + 33 1 44 07 83 01
Web page: http://centredeconomiesorbonne.univ-paris1.fr/
More information through EDIRC
Operational risk; generalized Pareto distribution; Picklands estimate; Hill estimate; expectation maximization algorithm; Monte Carlo simulations; VaR.;
Other versions of this item:
- Dominique Guegan & Bertrand Hassani & Cédric Naud, 2010. "An efficient threshold choice for operational risk capital computation," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00544342, HAL.
- Dominique Guegan & Bertrand Hassani & Cédric Naud, 2011. "An efficient threshold choice for operational risk capital computation," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00790217, HAL.
- 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.:
- 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.
- 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.
- repec:hal:journl:halshs-00639666 is not listed on IDEAS
- Dominique Guegan & Bertrand Hassani, 2011.
"A mathematical resurgence of risk management: an extreme modeling of expert opinions,"
UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers)
- Dominique Guegan & Bertrand K. Hassani, 2011. "A mathematical resurgence of risk management: an extreme modeling of expert opinions," Documents de travail du Centre d'Economie de la Sorbonne 11057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Pavel V. Shevchenko & Grigory Temnov, 2009. "Modeling operational risk data reported above a time-varying threshold," Papers 0904.4075, arXiv.org, revised Jul 2009.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lucie Label).
If references are entirely missing, you can add them using this form.