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Calculation of aggregate loss distributions

  • Pavel V. Shevchenko
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    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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    Paper provided by in its series Papers with number 1008.1108.

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    Date of creation: Aug 2010
    Date of revision:
    Publication status: Published in The Journal of Operational Risk 5(2), pp. 3-40, 2010
    Handle: RePEc:arx:papers:1008.1108
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    1. repec:spr:compst:v:69:y:2009:i:3:p:497-508 is not listed on IDEAS
    2. 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.
    3. Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(04), pages 519-529, December.
    4. Panjer, Harry H. & Willmot, Gordon E., 1986. "Computational aspects of recursive evaluation of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 113-116, January.
    5. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
    6. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
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