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A modified Panjer algorithm for operational risk capital calculations

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  • Dominique Guegan

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Bertrand Hassani

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

Abstract

Operational risk management inside banks and insurance companies is an important task. The computation of a risk measure associated to these kinds of risks lies in the knowledge of the so-called loss distribution function (LDF). Traditionally, this LDF is computed via Monte Carlo simulations or using the Panjer recursion, which is an iterative algorithm. In this paper, we propose an adaptation of this last algorithm in order to improve the computation of convolutions between Panjer class distributions and continuous distributions, by mixing the Monte Carlo method, a progressive kernel lattice and the Panjer recursion. This new hybrid algorithm does not face the traditional drawbacks. This simple approach enables us to drastically reduce the variance of the estimated value-at-risk associated with the operational risks and to lower the aliasing error we would have using Panjer recursion itself. Furthermore, this method is much less timeconsuming than a Monte Carlo simulation. We compare our new method with more sophisticated approaches already developed in operational risk literature.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00443846.

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Date of creation: Oct 2009
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Publication status: Published, Journal of Operational Risk, 2009, 4, 4, 53-72
Handle: RePEc:hal:cesptp:halshs-00443846

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Keywords: Operational risk ; Panjer algorithm ; Kernel ; numerical integration ; convolution.;

References

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  1. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
  2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  3. Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
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Cited by:
  1. Bertrand K. Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020293, HAL.
  2. Bertrand K Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Documents de travail du Centre d'Economie de la Sorbonne 14037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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