IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v64y2015icp364-379.html
   My bibliography  Save this article

Pricing guaranteed minimum/lifetime withdrawal benefits with various provisions under investment, interest rate and mortality risks

Author

Listed:
  • Dai, Tian-Shyr
  • Yang, Sharon S.
  • Liu, Liang-Chih

Abstract

Many variable annuity products associated with guaranteed minimum withdrawal benefit (GMWB) or its lifelong version, a guaranteed lifelong withdrawal benefit (GLWB), have enjoyed great market success in the United States and Asia. The interaction impacts among complex policy provisions and the randomness of the account value of the policy, the prevailing interest rate, as well as the mortality rate may significantly influence the evaluations of GMWBs/GMLBs, especially when the guaranteed payments are made over a long, or even a lifelong, horizon. To deal with aforementioned risk factors and policy provisions, this paper proposes a novel three-dimensional (3D) tree that can analyze how different policy provisions influence the evaluation of GMWB/GLWBs under investment interest rate, and mortality risks simultaneously. The orthogonalization method is used to convert correlated dynamics of the account value of the policy and the short-term interest rate into two independent processes that can be easily simulated by our 3D tree. Besides, the structure of our 3D tree is sophisticatedly designed to avoid the unstable (oscillating) pricing results phenomenon that has characterized many numerical pricing methods. Rigorous numerical experiments are given to analyze the interaction effects among policy provisions and the aforementioned risk factors on the evaluation of GMWBs/GLWBs.

Suggested Citation

  • Dai, Tian-Shyr & Yang, Sharon S. & Liu, Liang-Chih, 2015. "Pricing guaranteed minimum/lifetime withdrawal benefits with various provisions under investment, interest rate and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 364-379.
    • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:364-379
    DOI: 10.1016/j.insmatheco.2015.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668715000669
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2015.04.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    2. X. Sheldon Lin & Ken Seng Tan, 2003. "Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 72-91.
    3. Costabile, Massimo & Massabó, Ivar & Russo, Emilio, 2008. "A binomial model for valuing equity-linked policies embedding surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 873-886, June.
    4. Gabriella Piscopo & Steven Haberman, 2011. "The Valuation of Guaranteed Lifelong Withdrawal Benefit Options in Variable Annuity Contracts and the Impact of Mortality Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 59-76.
    5. Shen, Weixi & Xu, Huiping, 2005. "The valuation of unit-linked policies with or without surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 79-92, February.
    6. Lyuu,Yuh-Dauh, 2002. "Financial Engineering and Computation," Cambridge Books, Cambridge University Press, number 9780521781718, September.
    7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    8. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    9. Tian-Shyr Dai, 2009. "Efficient option pricing on stocks paying discrete or path-dependent dividends with the stair tree," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 827-838.
    10. 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.
    11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    12. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    13. Yang, Sharon S. & Dai, Tian-Shyr, 2013. "A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 231-242.
    14. Jingjiang Peng & Kwai Sun Leung & Yue Kuen Kwok, 2012. "Pricing guaranteed minimum withdrawal benefits under stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(6), pages 933-941, October.
    15. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    16. 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.
    17. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    18. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    19. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Post-Print hal-02896141, HAL.
    2. Karim Barigou & Lukasz Delong, 2020. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Papers 2007.08804, arXiv.org, revised Nov 2021.
    3. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    4. 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.
    5. 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.
    6. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2019. "Pricing and hedging GMWB in the Heston and in the Black–Scholes with stochastic interest rate models," Computational Management Science, Springer, vol. 16(1), pages 217-248, February.
    7. 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.
    8. Xiao Wei & Xingchi Gu, 2024. "Conditional Moment Matching and Stratified Approximation for Pricing and Hedging Periodic-Premium Variable Annuities," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-25, June.
    9. Paolo Angelis & Roberto Marchis & Antonio L. Martire & Emilio Russo, 2022. "A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 415-446, June.
    10. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    11. Andrea Molent, 2019. "Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model," Papers 1901.11296, arXiv.org, revised May 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paolo Angelis & Roberto Marchis & Antonio L. Martire & Emilio Russo, 2022. "A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 415-446, June.
    2. Yang, Sharon S. & Dai, Tian-Shyr, 2013. "A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 231-242.
    3. 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.
    4. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    5. Kang, Boda & Ziveyi, Jonathan, 2018. "Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 43-56.
    6. Maciej Augustyniak & Mathieu Boudreault, 2017. "Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 502-525, October.
    7. Hsieh, Ming-hua & Wang, Jennifer L. & Chiu, Yu-Fen & Chen, Yen-Chih, 2018. "Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 246-254.
    8. Fontana, Claudio & Rotondi, Francesco, 2023. "Valuation of general GMWB annuities in a low interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 142-167.
    9. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    10. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    11. Ignatieva, Katja & Song, Andrew & Ziveyi, Jonathan, 2016. "Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 286-300.
    12. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    13. Feng, Runhuan & Yi, Bingji, 2019. "Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 60-73.
    14. Yaowen Lu & Duy-Minh Dang, 2023. "A semi-Lagrangian $\epsilon$-monotone Fourier method for continuous withdrawal GMWBs under jump-diffusion with stochastic interest rate," Papers 2310.00606, arXiv.org.
    15. Charles Guy Njike Leunga & Donatien Hainaut, 2022. "Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 963-990, June.
    16. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    18. 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.
    19. Shen, Yang & Sherris, Michael & Ziveyi, Jonathan, 2016. "Valuation of guaranteed minimum maturity benefits in variable annuities with surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 127-137.
    20. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:364-379. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.