IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v99y2021icp63-78.html
   My bibliography  Save this article

Variable annuities: Market incompleteness and policyholder behavior

Author

Listed:
  • Moenig, Thorsten

Abstract

Variable annuities (VAs) are popular personal savings and investment vehicles with long-term guarantees. They include various exercise-dependent features, and the pricing, valuation and hedging of the guarantees depend critically on the investors’ decision making. I study whether the optimal exercise behavior of a VA investor is affected by market incompleteness, which arises since the VA generates payout profiles that intersect financial risk and idiosyncratic mortality risk and can thus not be (fully) replicated with traditional financial and insurance products.

Suggested Citation

  • Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:63-78
    DOI: 10.1016/j.insmatheco.2021.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668721000408
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2021.03.007?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. Ryan Donnelly & Sebastian Jaimungal & Dmitri H. Rubisov, 2014. "Valuing guaranteed withdrawal benefits with stochastic interest rates and volatility," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 369-382, February.
    2. Horneff, Vanya & Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph, 2015. "Optimal life cycle portfolio choice with variable annuities offering liquidity and investment downside protection," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 91-107.
    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. Gao, Jin & Ulm, Eric R., 2015. "Optimal allocation and consumption with guaranteed minimum death benefits, external income and term life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 87-98.
    5. Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Stamos, Michael Z., 2010. "Variable payout annuities and dynamic portfolio choice in retirement," Journal of Pension Economics and Finance, Cambridge University Press, vol. 9(2), pages 163-183, April.
    6. Thorsten Moenig & Daniel Bauer, 2016. "Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities," Review of Finance, European Finance Association, vol. 20(2), pages 759-794.
    7. 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.
    8. Jeffrey R. Brown & James M. Poterba, 2006. "Household Ownership of Variable Annuities," NBER Chapters, in: Tax Policy and the Economy, Volume 20, pages 163-191, National Bureau of Economic Research, Inc.
    9. 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.
    10. Jeffrey R. Brown & Olivia S. Mitchell & James M. Poterba, 2001. "The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program," NBER Chapters, in: Risk Aspects of Investment-Based Social Security Reform, pages 321-370, National Bureau of Economic Research, Inc.
    11. 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.
    12. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    13. Mahayni, Antje & Schneider, Judith C., 2012. "Variable annuities and the option to seek risk: Why should you diversify?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2417-2428.
    14. 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.
    15. Charupat, Narat & Milevsky, Moshe A., 2002. "Optimal asset allocation in life annuities: a note," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 199-209, April.
    16. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    17. Daniel Bauer & Jin Gao & Thorsten Moenig & Eric R. Ulm & Nan Zhu, 2017. "Policyholder Exercise Behavior in Life Insurance: The State of Affairs," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 485-501, October.
    18. Raimond Maurer & Olivia S. Mitchell & Ralph Rogalla & Vasily Kartashov, 2013. "Lifecycle Portfolio Choice With Systematic Longevity Risk and Variable Investment—Linked Deferred Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 649-676, September.
    19. Joachim Inkmann & Paula Lopes & Alexander Michaelides, 2011. "How Deep Is the Annuity Market Participation Puzzle?," The Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 279-319.
    20. Trottier, Denis-Alexandre & Godin, Frédéric & Hamel, Emmanuel, 2018. "Local Hedging Of Variable Annuities In The Presence Of Basis Risk," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 611-646, May.
    21. Delong, Łukasz, 2014. "Pricing and hedging of variable annuities with state-dependent fees," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 24-33.
    22. Etienne Chevalier & Thomas Lim & Ricardo Romo Romero, 2016. "Indifference fee rate for variable annuities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(4), pages 278-308, July.
    23. 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.
    24. 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.
    25. Massimo Costabile & Ivar Massabó & Emilio Russo, 2020. "Evaluating variable annuities with GMWB when exogenous factors influence the policy-holder's withdrawals," The European Journal of Finance, Taylor & Francis Journals, vol. 26(2-3), pages 238-257, February.
    26. Jin Sun & Pavel V. Shevchenko & Man Chung Fung, 2018. "The Impact of Management Fees on the Pricing of Variable Annuity Guarantees," Risks, MDPI, vol. 6(3), pages 1-20, September.
    27. Nikolay Gudkov & Katja Ignatieva & Jonathan Ziveyi, 2019. "Pricing of guaranteed minimum withdrawal benefits in variable annuities under stochastic volatility, stochastic interest rates and stochastic mortality via the componentwise splitting method," Quantitative Finance, Taylor & Francis Journals, vol. 19(3), pages 501-518, March.
    28. Ignatieva, Katja & Song, Andrew & Ziveyi, Jonathan, 2018. "Fourier Space Time-Stepping Algorithm For Valuing Guaranteed Minimum Withdrawal Benefits In Variable Annuities Under Regime-Switching And Stochastic Mortality," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 139-169, January.
    29. 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.
    30. 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.
    31. 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.
    32. Ulm, Eric R., 2020. "The effect of retirement taxation rules on the value of guaranteed lifetime withdrawal benefits," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 83-92, March.
    33. 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.
    34. X. Lin & Ken Tan & Hailiang Yang, 2009. "Pricing Annuity Guarantees Under a Regime-Switching Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 316-332.
    35. Christian Knoller & Gunther Kraut & Pascal Schoenmaekers, 2016. "On the Propensity to Surrender a Variable Annuity Contract: An Empirical Analysis of Dynamic Policyholder Behavior," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 979-1006, December.
    36. John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2011. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Public Care Aversion from Bequest Motives," Journal of Finance, American Finance Association, vol. 66(2), pages 519-561, April.
    37. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    38. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
    39. 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.
    40. Gabriella Piscopo & Philipp Rüede, 2018. "What if Variable Annuity Policyholders With Guaranteed Lifelong Withdrawal Benefit Were Rational?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(1), pages 203-217, March.
    41. Thorsten Moenig & Nan Zhu, 2018. "Lapse‐and‐Reentry in Variable Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 911-938, December.
    42. 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.
    43. Lee Lockwood, 2012. "Bequest Motives and the Annuity Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 226-243, April.
    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. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    5. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    6. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    7. 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.
    8. 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.
    9. Horneff, Vanya & Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph, 2015. "Optimal life cycle portfolio choice with variable annuities offering liquidity and investment downside protection," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 91-107.
    10. 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.
    11. 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.
    12. Daniel Bauer & Thorsten Moenig, 2023. "Cheaper by the bundle: The interaction of frictions and option exercise in variable annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 459-486, June.
    13. Jin Sun & Pavel V. Shevchenko & Man Chung Fung, 2018. "The Impact of Management Fees on the Pricing of Variable Annuity Guarantees," Risks, MDPI, vol. 6(3), pages 1-20, September.
    14. Maria Alexandrova & Nadine Gatzert, 2019. "What Do We Know About Annuitization Decisions?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 22(1), pages 57-100, March.
    15. 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).
    16. David Landriault & Bin Li & Dongchen Li & Yumin Wang, 2021. "High‐water mark fee structure in variable annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1057-1094, December.
    17. 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.
    18. 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.
    19. Mrad, Fatma & Hamdi, Haykel & Naoui, Kamel & Abid, Ilyes, 2023. "The GMWB guarantee embedded in Life Insurance Contracts: Fair Value Pricing Problem," Finance Research Letters, Elsevier, vol. 51(C).
    20. 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.

    More about this item

    Keywords

    Variable annuities; Optimal policyholder behavior; Market incompleteness; Lifecycle utility model; Guaranteed minimum withdrawal benefits;
    All these keywords.

    JEL classification:

    • 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:99:y:2021:i:c:p:63-78. 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.