Calculate Tail Quantiles of Compound Distributions

30 Pages Posted: 2 May 2019

See all articles by Azamat Abdymomunov

Azamat Abdymomunov

Federal Reserve Banks - Federal Reserve Bank of Richmond

Filippo Curti

Federal Reserve Banks - Federal Reserve Bank of Richmond

Hayden Kane

Federal Reserve Banks - Federal Reserve Bank of Richmond

Date Written: April 23, 2019

Abstract

We evaluate the performance of different approaches for estimating quantiles of compound 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 transform (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.

Keywords: compound distributions, fast Fourier transform (FFT), Monte Carlo, perturbative expansion correction (PEC), single-loss approximation (SLA)

Suggested Citation

Abdymomunov, Azamat and Curti, Filippo and Kane, Hayden, Calculate Tail Quantiles of Compound Distributions (April 23, 2019). Journal of Computational Finance, Vol. 22, No. 5, 2019. Available at SSRN: https://ssrn.com/abstract=3376709

Azamat Abdymomunov

Federal Reserve Banks - Federal Reserve Bank of Richmond ( email )

P.O. Box 27622
Richmond, VA 23261
United States

Filippo Curti

Federal Reserve Banks - Federal Reserve Bank of Richmond ( email )

P.O. Box 27622
Richmond, VA 23261
United States

Hayden Kane (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of Richmond ( email )

P.O. Box 27622
Richmond, VA 23261
United States

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