A0290
Title: A multiplier approach for nonparametric estimation of the extreme quantiles of compound frequency distributions
Authors: Helgard Raubenheimer - North-West University (South Africa) [presenting]
Riaan de Jongh - North-West University (South Africa)
Charl Pretorius - North-West University (South Africa)
Tertius de Wet - North-West University (South Africa)
Abstract: Estimating operational risk reserves is still widely done using the loss distribution approach. The accuracy of the estimation depends heavily on the accuracy with which the extreme quantiles of the aggregate loss distributions are estimated. Many approaches have been proposed to estimate the extreme quantiles of this compound distribution, amongst other approximations based on the underlying severity distribution, such as the single loss and perturbative approximations. Both the approximation approaches suggest using an even more extreme quantile of the underlying severity distribution. The estimation of these extreme quantiles lacks accuracy, so the obvious question is, why not estimate a less extreme or lower quantile of the severity distribution, hopefully with better accuracy, and then use a multiplier to approximate the extreme quantile? Using extreme value theory, first- and second-order multipliers are derived to estimate the extreme quantile of the severity distribution, which is approximated by the single loss and perturbative approximations. Nonparametric estimators for the multipliers are suggested and evaluated using a simulation study. The simulation study results suggest that the second-order multiplier, based on the second-order perturbative approximation, should be a good choice for practical applications.
