Can the single-loss approximation method compete with the standard monte carlo simulation technique?

In this paper we evaluate the single-loss approximation method for high-quantile loss estimation on the basis of SAS OpRisk Global Data. Due to its simplicity, the single-loss approximation method has become a popular tool for capital requirement calculation purposes in the financial services industry. As the single-loss approximation method requires some strict assumptions, the naive use of this method was criticized in a 2010 paper by Degen. Although we support this criticism, the single-loss approximation method yields astonishingly exact results for the underlying data set and our calibrated heavy-tailed lognormal loss severity model. We show in this paper that the value-at-risk (VaR) estimates by the single-loss approximation method are more accurate than the quantile estimates computed by a Monte Carlo simulation with one million losses. However, we find a significant 99.9%VaR underestimation for a medium-tailed gamma loss severity model.