Approaches to Calculate Tail Quantiles of Compound Distributions

The literature proposes several alternatives for estimating compound distributions, which are widely used for risk quantification in the banking and insurance industries. In this paper, we evaluate the accuracy and time-efficiency of different approaches for estimating quantiles of compound distributions. We focus on three approaches: 1) Single Loss Approximation (SLA), 2) Perturbative Expansion Correction (PEC), and 3) Fast Fourier Transform (FFT). We find that the PEC approach is an accurate and time-efficient methodology for sub-exponential distributions, but only for quantiles greater than the 95th. The SLA performs similarly, but only for tail quantiles greater than the 99th. Neither the SLA nor PEC approaches are accurate for non-sub-exponential distributions. The FFT approach consistently gives the most accurate estimates for every distribution, however it is substantially less time-efficient than the PEC or SLA approaches. We recommend applying the FFT approach for estimating lower quantiles and non-sub-exponential distributions. We contribute to the literature by providing comprehensive guidance for selecting an appropriate approach for various parametric distributions used in the banking and insurance industries