A new Algorithm for the Loss Distribution Function with applications to Operational Risk Management

Executive Summary Operational risk management inside banks and insurance companies is currently an important task. The computation of a risk measure associated to these kinds of risks lies on 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 VaR associated to the operational risks and, to lower the aliasing error we would have using Panjer recursion itself. Furthermore, this method is much less time-consuming than a Monte Carlo simulation. We compare our new method with more sophisticated approaches already developed in operational risk literature.