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Calculation of aggregate loss distributions

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  • Pavel V. Shevchenko
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    Abstract

    Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern computer processing power, these distributions can be calculated virtually exactly using numerical methods. This paper reviews numerical algorithms that can be successfully used to calculate the aggregate loss distributions. In particular Monte Carlo, Panjer recursion and Fourier transformation methods are presented and compared. Also, several closed-form approximations based on moment matching and asymptotic result for heavy-tailed distributions are reviewed.

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    File URL: http://arxiv.org/pdf/1008.1108
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1008.1108.

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    Date of creation: Aug 2010
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    Publication status: Published in The Journal of Operational Risk 5(2), pp. 3-40, 2010. www.journalofoperationalrisk.com
    Handle: RePEc:arx:papers:1008.1108

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    Web page: http://arxiv.org/

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    Cited by:
    1. Kensuke Ishitani & Kenichi Sato, 2013. "An Analytical Evaluation Method of the Operational Risk Using Fast Wavelet Expansion Techniques," Asia-Pacific Financial Markets, Springer, Springer, vol. 20(3), pages 283-309, September.
    2. Mora Valencia Andrés, 2014. "El uso de la distribución g-h en riesgo operativo," Contaduría y Administración:Revista Internacional, Accounting and Management: International Journal, Accounting and Management: International Journal, vol. 59(1), pages 123-148, enero-mar.

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