Analytic valuation of guaranteed lifetime withdrawal benefits with a modified ratchet

Darcy Harcourt, Toby Daglish and Eric R. Ulm

Insurance: Mathematics and Economics, 2024, vol. 118, issue C, 59-71

Abstract: Guaranteed Lifetime Withdrawal Benefits (GLWBs) are an increasingly popular add-on to Variable Annuities, offering a guaranteed stream of payments for the remainder of the policyholder's life. GLWBs have typically been priced using numerical methods such as finite difference schemes or Monte Carlo simulations; obtaining accurate and precise solutions using these methods can be very computationally expensive. In this paper, we extend an existing method for analytic pricing of these policies to a more general fee structure. We introduce a novel variation on the commonly offered ratchet rider that more directly addresses policyholder motivation around lapse-and-reentry behaviour. We then modify our pricing method to accommodate this new rider and compare it to the existing annual ratchet with respect to a policyholder's incentive to lapse such a policy.

Keywords: Variable annuities; Guaranteed lifetime withdrawal benefits; Analytic solution; Geometric Brownian motion with affine drift (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:118:y:2024:i:c:p:59-71

DOI: 10.1016/j.insmatheco.2024.06.001

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