Approaches to Calculate Tail Quantiles of Compound Distributions

52 Pages Posted: 13 Mar 2017

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: March 10, 2017

Abstract

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.

Keywords: Panjer Recursion, Monte Carlo, Single Loss Approximation

JEL Classification: C15, C63, G21, G22

Suggested Citation

Abdymomunov, Azamat and Curti, Filippo and Kane, Hayden, Approaches to Calculate Tail Quantiles of Compound Distributions (March 10, 2017). Available at SSRN: https://ssrn.com/abstract=2930965 or http://dx.doi.org/10.2139/ssrn.2930965

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

Register to save articles to
your library

Register

Paper statistics

Downloads
51
Abstract Views
297
rank
388,344
PlumX Metrics