What if Variable Annuity Policyholders With Guaranteed Lifelong Withdrawal Benefit Were Rational?

• DOI: http://doi.org/10.1111/jori.12146
• Published date: 01 March 2018
• Date: 01 March 2018
• Author: Philipp Rüede,Gabriella Piscopo

©2016 The Journal of Risk and Insurance. Vol.85, No. 1, 203–217 (2018).

DOI: 10.1111/jori.12146

What if Variable Annuity Policyholders With

Guaranteed Lifelong Withdrawal Benefit Were

Rational?

Gabriella Piscopo

Philipp R ¨

uede

Abstract

This article examines the lapse risk inherent to the guaranteed lifelong with-

drawal benefit option embedded in a variable annuity product valuated from

a pure derivatives perspective, that is, as a Bermudian option given to the

policyholder. We assume rational behavior and quantify the potential im-

pact of the lapse risk, defined as the difference between no lapse and optimal

lapsing. We develop a sensitivity analysis that shows how the value of the

productvaries with the key parameters, and calculate the fair fee using Monte

Carlo simulations. Empirical analyses are performed and numerical results

are provided.

Introduction

Variableannuities (VA) are unit-linked annuity contracts that provide participation in

the stock market with partial protection against downside movements. The complex-

ity of this hybrid product, caused by mortality, longevity, behavioral, financial risks,

and its long duration and path dependency cannot be ignored. Since the product’s

introduction, some embedded guarantees have been offered with these policies; typ-

ically,there is no up-front fee but a regular deduction of units from the account value

during the lifetime of the policy. One of the most common is the guaranteed mini-

mum withdrawal benefit (GMWB) option, which gives the policyholder the option

to withdraw a prespecified annual amount even if the account value has fallen below

this amount. The latest variant of the GMWB is the guaranteed lifelong withdrawal

benefit option (GLWB). This option offers a lifelong withdrawal guarantee. There-

fore, there is no limit to the total amount that can be withdrawn over the term of the

policy because if the account value becomes zero while the insured is still alive, the

policy-holder can continue to withdraw the guaranteed annual amount until death.

The actuarial literature has tended to focus on the GMWB (Milevsky and Salisbury,

Gabriella Piscopo is at the Department of Economics, University of Genoa, Via Vivaldi, 16126

Genoa, Italy. Piscopo can be contacted via e-mail: piscopo@economia.unige.it. Philipp Rüede

is at SwissRe, Zurich. R¨

uede can be contacted via e-mail: philipp.rueede@me.co. Any opinions

expressed in this article are their own and not necessarily those of their employers.

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