Calculation of aggregate loss distributions
For practitioners in operational risk, this is a tutorial review of existing methods, offering no novel contributions.
This paper reviews numerical algorithms for calculating aggregate loss distributions in operational risk, comparing Monte Carlo, Panjer recursion, and Fourier transformation methods, as well as closed-form approximations. No new results or concrete numbers are provided.
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.