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Valuation of a Guaranteed Minimum Income Benefit

Author

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  • Claymore Marshall
  • Mary Hardy
  • David Saunders

Abstract

With a deferred variable annuity the policyholder pays an upfront premium to the insurance company, which is then invested in the financial markets for many years (the accumulation phase) until the policyholder decides to convert their investment (often at retirement age) into a stream of variable annuity payments. A Guaranteed Minimum Income Benefit (GMIB) is an option that may be included at inception of a variable annuity contract that, in exchange for small fees charged by the insurer, gives the policyholder a right to receive a guaranteed minimum level of annuity payments upon annuitization. A GMIB is an attractive option because it protects the policyholder’s investment against poor market performance during the accumulation phase.The value of a GMIB is affected by investment account returns, interest rates, and mortality. The intention of this paper is to value a GMIB in a complete market, focusing on the sensitivity of the GMIB value to the financial variables. Mortality is not incorporated into the valuation. We present a comprehensive sensitivity analysis of the model employed. We decompose a GMIB payoff, which is rather complicated, to analyze what drives the value of a GMIB. Our approach offers a simple but effective way for insurers to measure the value of the GMIBs they offer, and it provides insights into the risk management of GMIBs and other guarantees that provide similar payoffs. Our model suggests that the fee rates charged by insurance companies for the GMIB option may be too low.

Suggested Citation

  • Claymore Marshall & Mary Hardy & David Saunders, 2010. "Valuation of a Guaranteed Minimum Income Benefit," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 38-58.
    • Handle: RePEc:taf:uaajxx:v:14:y:2010:i:1:p:38-58
    DOI: 10.1080/10920277.2010.10597576
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    Citations

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    Cited by:

    1. 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.
    2. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    3. Bohnert, Alexander & Born, Patricia & Gatzert, Nadine, 2014. "Dynamic hybrid products in life insurance: Assessing the policyholders’ viewpoint," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 87-99.
    4. Dong, Bing & Xu, Wei & Sevic, Aleksandar & Sevic, Zeljko, 2020. "Efficient willow tree method for variable annuities valuation and risk management☆," International Review of Financial Analysis, Elsevier, vol. 68(C).
    5. Gan Guojun & Valdez Emiliano A., 2017. "Valuation of large variable annuity portfolios: Monte Carlo simulation and synthetic datasets," Dependence Modeling, De Gruyter, vol. 5(1), pages 354-374, December.
    6. 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.
    7. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior," Tinbergen Institute Discussion Papers 15-008/IV/DSF85, Tinbergen Institute.
    8. Deelstra, Griselda & Rayée, Grégory, 2013. "Pricing Variable Annuity Guarantees in a local volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 650-663.
    9. 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.
    10. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    11. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    12. Riley Jones & Adriana Ocejo, 2019. "Assessing Guaranteed Minimum Income Benefits and Rationality of Exercising Reset Options in Variable," Papers 1911.06123, arXiv.org.
    13. Bernard, Carole & Kwak, Minsuk, 2016. "Semi-static hedging of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 173-186.
    14. 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.
    15. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    16. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.

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