An efficient threshold choice for operational risk capital computation
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
|Date of creation:||Nov 2010|
|Date of revision:||Nov 2011|
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- 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.
- 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.
- Pavel V. Shevchenko & Grigory Temnov, 2009. "Modeling operational risk data reported above a time-varying threshold," Papers 0904.4075, arXiv.org, revised Jul 2009.
- 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.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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