Tail Index-Linked Annuity: A Longevity Risk Sharing Retirement Plan

27 Pages Posted: 11 Sep 2020

See all articles by An Chen

An Chen

University of Ulm

Hong Li

Warren Centre for Actuarial Studies and Research, University of Manitoba

Mark Schultze

affiliation not provided to SSRN

Date Written: July 31, 2020

Abstract

This paper proposes an innovative retirement product with a focus on longevity risk sharing, a contract we refer to as tail index-linked annuity (TILA). Specifically, the proposed TILA pays out variable annual payments, which will be equal to a regular nominal amount when a reference survival index is lower than a predetermined threshold (i.e., normal evolution of longevity risk), and a reduced, index-dependent payment when the threshold is passed (i.e., highly unfavorable evolution of longevity risk). The proposed TILA aims at not only improving the benefits of the policyholders, which has been the focus in recent literature on innovative retirement products, but also reducing the longevity risk exposure of the insurer, particularly for advanced retirement ages. Using real-world mortality data and stochastic multi-population mortality model, we find that the proposed TILA leads to higher expected lifetime utility than regular annuities for policyholders with different degrees of risk aversions. Meanwhile, numerical analysis shows that the proposed TILA could greatly mitigate the solvency risk of the insurer, leading to substantially lower loss probability and expected (tail-) loss than regular annuities in the presence of longevity shock, and therefore could reduce the insurer's required solvency capital under latest solvency regulations.

Keywords: indexed annuity, longevity risk, multi-population mortality, retirement product design

JEL Classification: G22, G13, J11

Suggested Citation

Chen, An and Li, Hong and Schultze, Mark, Tail Index-Linked Annuity: A Longevity Risk Sharing Retirement Plan (July 31, 2020). Available at SSRN: https://ssrn.com/abstract=3664433 or http://dx.doi.org/10.2139/ssrn.3664433

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Hong Li (Contact Author)

Warren Centre for Actuarial Studies and Research, University of Manitoba ( email )

638 Drake Centre, 181 Freedman Crescent
Winnipeg, MB R3T 2N2
Canada

HOME PAGE: http://https://hongliecon.weebly.com/

Mark Schultze

affiliation not provided to SSRN

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