Calculation of aggregate loss distributions

TL;DR

This paper reviews numerical algorithms like Monte Carlo, Panjer recursion, and Fourier transforms for calculating aggregate loss distributions in operational risk, comparing their effectiveness and discussing approximation methods.

Contribution

It provides a comprehensive review and comparison of numerical and approximation methods for calculating aggregate loss distributions in operational risk modeling.

Findings

Monte Carlo, Panjer recursion, and Fourier transform methods are effective for calculating loss distributions.

Closed-form approximations based on moment matching and asymptotic analysis are also discussed.

The paper highlights the strengths and limitations of each computational approach.

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.