IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v117y2024icp154-169.html
   My bibliography  Save this article

Coping with longevity via hedging: Fair dynamic valuation of variable annuities

Author

Listed:
  • Chen, Ze
  • Feng, Runhuan
  • Li, Hong
  • Yang, Tianyu

Abstract

This paper introduces a fair valuation framework for pricing variable annuity liabilities and their embedded guarantee riders within a dynamic multi-period context. We focus on variable annuities featuring the Guaranteed Lifetime Withdrawal Benefit (GLWB) rider, which exposes policyholders to both financial and longevity risks. We employ a fair dynamic valuation method that is market-consistent, actuarially-consistent, and time-consistent. Our findings demonstrate that this approach effectively establishes fair management fee rates, aligning with prior research and industry surveys. Furthermore, we highlight the potential for significant reductions in liability valuation, and consequently, GLWB rider pricing, through effective management of longevity risk within the insurer's net liability.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:117:y:2024:i:c:p:154-169
    DOI: 10.1016/j.insmatheco.2024.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668724000556
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2024.04.005?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. Feng, Runhuan & Jing, Xiaochen, 2017. "Analytical valuation and hedging of variable annuity guaranteed lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 36-48.
    2. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672, December.
    3. Thomson, Robert J., 2005. "The pricing of liabilities in an incomplete market using dynamic mean-variance hedging," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 441-455, June.
    4. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    5. Kevin Dowd & Andrew Cairns & David Blake & Guy Coughlan & Marwa Khalaf-Allah, 2011. "A Gravity Model of Mortality Rates for Two Related Populations," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 334-356.
    6. Chen, Ze & Chen, Bingzheng & Dhaene, Jan & Yang, Tianyu, 2021. "Fair dynamic valuation of insurance liabilities via convex hedging," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 1-13.
    7. 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.
    8. Paul Dawson & Kevin Dowd & Andrew J. G. Cairns & David Blake, 2010. "Survivor Derivatives: A Consistent Pricing Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 579-596, September.
    9. Karim Barigou & Jan Dhaene, 2019. "Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(2), pages 163-187, February.
    10. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    11. Runhuan Feng & Guojun Gan & Ning Zhang, 2022. "Variable annuity pricing, valuation, and risk management: a survey," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(10), pages 867-900, November.
    12. 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.
    13. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    14. Amy Kessler, 2021. "New Solutions to an Age-Old Problem: Innovative Strategies for Managing Pension and Longevity Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(S1), pages 7-24, February.
    15. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
    16. Delong, Łukasz & Dhaene, Jan & Barigou, Karim, 2019. "Fair Valuation Of Insurance Liability Cash-Flow Streams In Continuous Time: Applications," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 299-333, May.
    17. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    18. 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.
    19. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    20. Barigou, Karim & Chen, Ze & Dhaene, Jan, 2019. "Fair dynamic valuation of insurance liabilities: Merging actuarial judgement with market- and time-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 19-29.
    21. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    22. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
    23. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    24. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    25. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    26. 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.
    27. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    28. 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.
    29. Alex Cowley & J. David Cummins, 2005. "Securitization of Life Insurance Assets and Liabilities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 193-226, June.
    30. Anna Rita Bacinello & Pietro Millossovich & Alvaro Montealegre, 2016. "The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(5), pages 446-465, May.
    31. Tsanakas, Andreas & Wüthrich, Mario V. & Černý, Aleš, 2013. "Market Value Margin Via Mean–Variance Hedging," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 301-322, September.
    32. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    33. 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.
    34. Kevin Dowd & Andrew J. G. Cairns & David Blake, 2021. "Hedging Annuity Risks with the Age-Period-Cohort Two-Population Gravity Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(S1), pages 170-181, February.
    35. 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.
    36. Chen, An & Li, Hong & Schultze, Mark B., 2023. "Optimal longevity risk transfer under asymmetric information," Economic Modelling, Elsevier, vol. 120(C).
    37. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    38. repec:cup:bracjl:v:24:y:2018:i::p:-_1 is not listed on IDEAS
    39. Linders, Daniël, 2023. "The 3-step hedge-based valuation: fair valuation in the presence of systematic risks," ASTIN Bulletin, Cambridge University Press, vol. 53(2), pages 418-442, May.
    40. Chen, An & Li, Hong & Schultze, Mark, 2022. "Collective longevity swap: A novel longevity risk transfer solution and its economic pricing," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 227-249.
    41. Ze Chen & Bingzheng Chen & Jan Dhaene, 2020. "Fair dynamic valuation of insurance liabilities: a loss averse convex hedging approach," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(9), pages 792-818, October.
    42. Li, Hong, 2018. "Dynamic Hedging Of Longevity Risk: The Effect Of Trading Frequency," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 197-232, January.
    43. Li, Johnny Siu-Hang & Luo, Ancheng, 2012. "Key Q-Duration: A Framework for Hedging Longevity Risk," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 413-452, November.
    44. Xiaolin Luo & Pavel V. Shevchenko, 2014. "Valuation of Variable Annuities with Guaranteed Minimum Withdrawal and Death Benefits via Stochastic Control Optimization," Papers 1411.5453, arXiv.org, revised Apr 2015.
    Full references (including those not matched with items on IDEAS)

    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. Chen, Ze & Chen, Bingzheng & Dhaene, Jan & Yang, Tianyu, 2021. "Fair dynamic valuation of insurance liabilities via convex hedging," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 1-13.
    2. David Blake & Marco Morales & Jing Ai & Patrick L. Brockett & Linda L. Golden & Wei Zhu, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 319-343, April.
    3. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    4. 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.
    5. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    6. Chen, An & Li, Hong & Schultze, Mark, 2022. "Collective longevity swap: A novel longevity risk transfer solution and its economic pricing," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 227-249.
    7. 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.
    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. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    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. 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.
    12. 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.
    13. Barigou, Karim & Chen, Ze & Dhaene, Jan, 2019. "Fair dynamic valuation of insurance liabilities: Merging actuarial judgement with market- and time-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 19-29.
    14. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    15. David Blake & Christophe Courbage & Richard MacMinn & Michael Sherris, 2011. "Longevity Risk and Capital Markets: The 2010–2011 Update," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(4), pages 489-500, October.
    16. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2021. "Mortality/Longevity Risk-Minimization with or without Securitization," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    17. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Working Papers hal-02896141, HAL.
    18. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Post-Print hal-02896141, HAL.
    19. Pavel V. Shevchenko & Xiaolin Luo, 2016. "Valuation of Variable Annuities with Guaranteed Minimum Withdrawal Benefit under Stochastic Interest Rate," Papers 1602.03238, arXiv.org, revised Jan 2017.
    20. 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.

    More about this item

    Keywords

    Fair dynamic valuation; Market-consistency; Variable annuity; Longevity risk; Convex hedging;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    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:117:y:2024:i:c:p:154-169. 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.