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Optimal initiation of a GLWB in a variable annuity: no arbitrage approach

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  • H. Huang
  • M. A. Milevsky
  • T. S. Salisbury

Abstract

This paper offers a financial economic perspective on the optimal time (and age) at which the owner of a Variable Annuity (VA) policy with a Guaranteed Living Withdrawal Benefit (GLWB) rider should initiate guaranteed lifetime income payments. We abstract from utility, bequest and consumption preference issues by treating the VA as liquid and tradable. This allows us to use an American option pricing framework to derive a so-called optimal initiation region. Our main practical finding is that given current design parameters in which volatility (asset allocation) is restricted to less than 20%, while guaranteed payout rates (GPR) as well as bonus (roll-up) rates are less than 5%, GLWBs that are in-the-money should be turned on by the late 50s and certainly the early 60s. The exception to the rule is when a non-constant GPR is about to increase (soon) to a higher age band, in which case the optimal policy is to wait until the new GPR is hit and then initiate immediately. Also, to offer a different perspective, we invert the model and solve for the bonus (roll-up) rate that is required to justify delaying initiation at any age. We find that the required bonus is quite high and more than what is currently promised by existing products. Our methodology and results should be of interest to researchers as well as to the individuals that collectively have over \$1 USD trillion in aggregate invested in these products. We conclude by suggesting that much of the non-initiation at older age is irrational (which obviously benefits the insurance industry.)

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  • H. Huang & M. A. Milevsky & T. S. Salisbury, 2013. "Optimal initiation of a GLWB in a variable annuity: no arbitrage approach," Papers 1304.1821, arXiv.org.
    • Handle: RePEc:arx:papers:1304.1821
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    References listed on IDEAS

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    3. Feng, Runhuan & Huang, Huaxiong, 2016. "Statutory financial reporting for variable annuity guaranteed death benefits: Market practice, mathematical modeling and computation," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 54-64.
    4. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    5. Bacinello, Anna Rita & Maggistro, Rosario & Zoccolan, Ivan, 2024. "Risk-neutral valuation of GLWB riders in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 1-14.
    6. Chen, Ze & Feng, Runhuan & Li, Hong & Yang, Tianyu, 2024. "Coping with longevity via hedging: Fair dynamic valuation of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 154-169.
    7. Xu, Wei & Chen, Yuehuan & Coleman, Conrad & Coleman, Thomas F., 2018. "Moment matching machine learning methods for risk management of large variable annuity portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 1-20.
    8. Hainaut, Donatien & Deelstra, Griselda, 2014. "Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 124-146.
    9. Steinorth, Petra & Mitchell, Olivia S., 2015. "Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 246-258.
    10. Runhuan Feng & Jan Vecer, 2017. "Risk based capital for guaranteed minimum withdrawal benefit," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 471-478, March.

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