Approximations of Value-at-Risk As an Extreme Quantile of a Random Sum of Heavy-Tailed Random Variables

Abstract

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or more specifically, subexponential random variables. A key application of this approximation is the calculation of operational VaR (value at risk) for financial institutions, to determine operational risk capital requirements. The paper follows work by Bocker & Kluppelberg (2005) & Bocker and Sprittulla (2006) and makes several advances. These include two new approximations of VaR and an extension to multiple loss types where the VaR relates to a sum of random sums, each of which is defined by different distributions. The proposed approximations are assessed via a simulation study.