Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk

Catalina Bolancé and Montserrat Guillen
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Catalina Bolancé: Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, 08007 Barcelona, Spain
Montserrat Guillen: Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, 08007 Barcelona, Spain

Risks, 2021, vol. 9, issue 4, 1-23

Abstract: A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of age-at-death conditional on having survived a certain age is fundamental for evaluating the risk of lifetime insurance. Our proposal combines a parametric distributions with nonparametric sample information, leading to obtain an asymptotic unbiased estimator of extreme quantiles for alternative distributions with different right tail shape, i.e., heavy tail or exponential tail. A method for estimating the longevity risk of a continuous temporary annuity is also shown. We illustrate our proposal with an application to the official age-at-death statistics of the population in Spain.

Keywords: extreme quantile; kernel estimation; extreme value distribution; lifetime annuity (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:9:y:2021:i:4:p:77-:d:536622

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