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Variable Annuity with GMWB: surrender or not, that is the question

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  • Xiaolin Luo
  • Pavel Shevchenko

Abstract

Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with Guaranteed Minimum Withdrawal Benefit (GMWB) is an optimal stochastic control problem. The surrender feature available in marketed products allows termination of the contract before maturity, making it also an optimal stopping problem. Although the surrender feature is quite common in variable annuity contracts, there appears to be no published analysis and results for this feature in GMWB under optimal policyholder behaviour - results found in the literature so far are consistent with the absence of such a feature. Also, it is of practical interest to see how the much simpler bang-bang strategy, although not optimal for GMWB, compares with optimal GMWB strategy with surrender option. In this paper we extend our recently developed algorithm (Luo and Shevchenko 2015a) to include surrender option in GMWB and compare prices under different policyholder strategies: optimal, static and bang-bang. Results indicate that following a simple but sub-optimal bang-bang strategy does not lead to significant reduction in the price or equivalently in the fee, in comparison with the optimal strategy. We observed that the extra value added by the surrender option could add very significant value to the GMWB contract. We also performed calculations for static withdrawal with surrender option, which is the same as bang-bang minus the "no-withdrawal" choice. We find that the fee for such contract is only less than 1% smaller when compared to the case of bang-bang strategy, meaning that th "no-withdrawal" option adds little value to the contract.

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  • Xiaolin Luo & Pavel Shevchenko, 2015. "Variable Annuity with GMWB: surrender or not, that is the question," Papers 1507.08738, arXiv.org.
    • Handle: RePEc:arx:papers:1507.08738
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    References listed on IDEAS

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    1. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    2. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
    3. Huang, Yao Tung & Kwok, Yue Kuen, 2014. "Analysis of optimal dynamic withdrawal policies in withdrawal guarantee products," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 19-43.
    4. Xiaolin Luo & Pavel V. Shevchenko, 2014. "Fast and Simple Method for Pricing Exotic Options using Gauss-Hermite Quadrature on a Cubic Spline Interpolation," Papers 1408.6938, arXiv.org, revised Dec 2014.
    5. 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.
    6. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
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    Cited by:

    1. Shevchenko, Pavel V. & Luo, Xiaolin, 2017. "Valuation of variable annuities with Guaranteed Minimum Withdrawal Benefit under stochastic interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 104-117.
    2. Huansang Xu & Ruyi Liu & Marek Rutkowski, 2023. "Equity Protection Swaps: A New Type of Investment Insurance for Holders of Superannuation Accounts," Papers 2305.09472, arXiv.org, revised Apr 2024.
    3. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2019. "Gaussian Process Regression for Pricing Variable Annuities with Stochastic Volatility and Interest Rate," Papers 1903.00369, arXiv.org, revised Jul 2019.
    4. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework," Risks, MDPI, vol. 4(3), pages 1-31, July.

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