Simulation of the annual loss distribution in operational risk via Panjer recursions and Volterra integral equations for value-at-risk and expected shortfall estimation

Abstract

Following the Loss Distribution Approach (LDA), this article develops two procedures for the simulation of an annual loss distribution for the modeling of operational risk. First, we provide an overview of the typical compound-process LDA used widely in operational risk modeling, before expanding upon the current literature on the evaluation and simulation of annual loss distributions. We present two novel Monte Carlo simulation procedures. In doing so, we make use of Panjer recursions and the Volterra integral equation of the second kind to reformulate the problem of the evaluation of the density of a random sum as the calculation of an expectation. We demonstrate the use of importance sampling and transdimensional Markov chain Monte Carlo algorithms to efficiently evaluate this expectation. We further demonstrate their use in the calculation of value-at-risk and expected shortfall.