Calculate tail quantiles of compound distributions

Azamat Abdymomunov, Filippo Curti and Hayden Kane

Abstract

We evaluate the performance of different approaches for estimating quantiles of com- pound distributions, which are widely used for risk quantification in the banking and insurance industries. We focus on three approaches: (1) single-loss approximation (SLA), (2) perturbative expansion correction (PEC) and (3) the fast Fourier trans- form (FFT). We demonstrate that both the SLA and PEC approaches are accurate only for tail quantiles of subexponential distributions. The PEC approach produces accurate estimates for quantiles greater than 95, while the SLA can only do this for quantiles greater than 99.9. Thus, the PEC approach dominates the SLA approach. The FFT approach consistently gives the most accurate estimates for every distribution. However, the FFT approach is substantially less time efficient than the PEC or SLA approaches, which are closed-form solutions. We contribute to the literature by providing practical guidance on selecting appropriate approaches for the various parametric distributions and quantiles used in the banking and insurance industries.