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Analytic valuation of guaranteed lifetime withdrawal benefits with a modified ratchet

Author

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  • Harcourt, Darcy
  • Daglish, Toby
  • Ulm, Eric R.

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.

Suggested Citation

  • Harcourt, Darcy & Daglish, Toby & Ulm, Eric R., 2024. "Analytic valuation of guaranteed lifetime withdrawal benefits with a modified ratchet," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 59-71.
    • Handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:59-71
    DOI: 10.1016/j.insmatheco.2024.06.001
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    References listed on IDEAS

    as
    1. Feng, Runhuan & Jing, Xiaochen, 2017. "Analytical valuation and hedging of variable annuity guaranteed lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 36-48.
    2. Ulm, Eric R., 2014. "Analytic solution for ratchet guaranteed minimum death benefit options under a variety of mortality laws," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 14-23.
    3. Daniel Dufresne, 2007. "Fitting combinations of exponentials to probability distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 23-48, January.
    4. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    5. Christian Knoller & Gunther Kraut & Pascal Schoenmaekers, 2016. "On the Propensity to Surrender a Variable Annuity Contract: An Empirical Analysis of Dynamic Policyholder Behavior," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 979-1006, December.
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    More about this item

    Keywords

    Variable annuities; Guaranteed lifetime withdrawal benefits; Analytic solution; Geometric Brownian motion with affine drift;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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