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The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits

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  • Eric R. Ulm

Abstract

Variable annuity contracts frequently have many options and option‐like features embedded in the contracts. Some are obvious, such as guaranteed minimum death benefits (GMDBs), while others are less obviously option‐like. In this article, we consider the effect of the real option to transfer funds between fixed and variable accounts. If a GMDB rider is considered in isolation, it is sometimes in the policyholder's interest to transfer to the fixed fund if the fixed fund earns less than the variable fund in a risk‐neutral world. On the other hand, the option to transfer will not be used if the entire annuity and rider are considered together.

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  • Eric R. Ulm, 2006. "The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 43-69, March.
    • Handle: RePEc:bla:jrinsu:v:73:y:2006:i:1:p:43-69
    DOI: 10.1111/j.1539-6975.2006.00165.x
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    Cited by:

    1. Ulm, Eric, 2020. "Analytic Valuation of GMDB Options with Utility Based Asset Allocation," Working Paper Series 21060, Victoria University of Wellington, School of Economics and Finance.
    2. Seyed Amir Hejazi & Kenneth R. Jackson, 2016. "A Neural Network Approach to Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1606.07831, arXiv.org.
    3. Anne MacKay & Maciej Augustyniak & Carole Bernard & Mary R. Hardy, 2017. "Risk Management of Policyholder Behavior in Equity-Linked Life Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 661-690, June.
    4. Seyed Amir Hejazi & Kenneth R. Jackson & Guojun Gan, 2017. "A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1701.04134, arXiv.org.
    5. 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.
    6. Liang, Xiaoqing & Tsai, Cary Chi-Liang & Lu, Yi, 2016. "Valuing guaranteed equity-linked contracts under piecewise constant forces of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 150-161.
    7. Hejazi, Seyed Amir & Jackson, Kenneth R., 2016. "A neural network approach to efficient valuation of large portfolios of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 169-181.
    8. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2015. "Geometric stopping of a random walk and its applications to valuing equity-linked death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 313-325.
    9. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    10. 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.
    11. Yichen Han & Dongchen Li & Kun Fan & Jiaxin Wan & Luyan Li, 2024. "Valuation of a Mixture of GMIB and GMDB Variable Annuity," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    12. Wang, Yayun & Zhang, Zhimin & Yu, Wenguang, 2021. "Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    13. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 73-92.
    14. Gao, Jin & Ulm, Eric R., 2012. "Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 586-598.
    15. Yaodi Yong & Hailiang Yang, 2021. "Valuation of Cliquet-Style Guarantees with Death Benefits in Jump Diffusion Models," Mathematics, MDPI, vol. 9(16), pages 1-21, August.

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