A modified Panjer algorithm for operational risk capital calculations
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.
|Date of creation:||Oct 2009|
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|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00443846|
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- 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.
- Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
- 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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