IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v6y2018i3p103-d170856.html
   My bibliography  Save this article

The Impact of Management Fees on the Pricing of Variable Annuity Guarantees

Author

Listed:
  • Jin Sun

    (Faculty of Sciences, University of Technology Sydney, Ultimo 2007, Australia
    Data61, CSIRO—Commonwealth Scientific and Industrial Research Organisation, Canberra 2601, Australia)

  • Pavel V. Shevchenko

    (Department of Actuarial Studies and Business Analytics, Macquarie University, North Ryde 2109, Australia)

  • Man Chung Fung

    (Data61, CSIRO—Commonwealth Scientific and Industrial Research Organisation, Canberra 2601, Australia)

Abstract

Variable annuities, as a class of retirement income products, allow equity market exposure for a policyholder’s retirement fund with optional guarantees to limit the downside risk of the market. Management fees andguarantee insurance fees are charged respectively for the market exposure and for the protection from the downside risk. We investigate the pricing of variable annuity guarantees under optimal withdrawal strategies when management fees are present. We consider from both policyholder’s and insurer’s perspectives optimal withdrawal strategies and calculate the respective fair insurance fees. We reveal a discrepancy where the fees from the insurer’s perspective can be significantly higher due to the management fees serving as a form of market friction. Our results provide a possible explanation of lower guarantee insurance fees observed in the market than those predicted from the insurer’s perspective. Numerical experiments are conducted to illustrate the results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:103-:d:170856
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/6/3/103/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/6/3/103/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic approximations of risk measures for variable annuity guaranteed benefits with dynamic policyholder behavior," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485229, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    2. Parsiad Azimzadeh & Peter A. Forsyth, 2015. "The existence of optimal bang-bang controls for GMxB contracts," Papers 1502.05743, arXiv.org, revised Nov 2015.
    3. Zhenyu Cui & Runhuan Feng & Anne MacKay, 2017. "Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 458-483, July.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    5. 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.
    6. 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.
    7. A. C. Belanger & P. A. Forsyth & G. Labahn, 2009. "Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 451-496.
    8. Agapova, Anna, 2011. "Conventional mutual index funds versus exchange-traded funds," Journal of Financial Markets, Elsevier, vol. 14(2), pages 323-343, May.
    9. 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.
    10. James M. Poterba & John B. Shoven, 2002. "Exchange-Traded Funds: A New Investment Option for Taxable Investors," American Economic Review, American Economic Association, vol. 92(2), pages 422-427, May.
    11. Kling, Alexander & Ruez, Frederik & Ruß, Jochen, 2011. "The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 511-545, November.
    12. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
    13. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    14. 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.
    15. Feng, Runhuan & Volkmer, Hans W., 2012. "Analytical calculation of risk measures for variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 636-648.
    16. Hyndman, Cody B. & Wenger, Menachem, 2014. "Valuation perspectives and decompositions for variable annuities with GMWB riders," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 283-290.
    17. 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.
    18. Runhuan Feng & Jan Vecer, 2017. "Risk based capital for guaranteed minimum withdrawal benefit," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 471-478, March.
    19. 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.
    20. Bacinello, Anna Rita & Ortu, Fulvio, 1996. "Fixed income linked life insurance policies with minimum guarantees: Pricing models and numerical results," European Journal of Operational Research, Elsevier, vol. 91(2), pages 235-249, June.
    21. 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.
    22. 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.
    23. 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.
    24. 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. 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).
    2. 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.
    3. Dionne, Georges & Fenou, Akouété & Mnasri, Mohamed, 2024. "Insurers’ M&A in the United States during the 1990-2022 period: Is the Fed monetary policy a causal factor," Working Papers 24-2, HEC Montreal, Canada Research Chair in Risk Management, revised 16 Jul 2024.
    4. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    5. Anne MacKay & Adriana Ocejo, 2022. "Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1021-1049, June.

    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. Jin Sun & Pavel V. Shevchenko & Man Chung Fung, 2017. "A note on the impact of management fees on the pricing of variable annuity guarantees," Papers 1705.03787, arXiv.org, revised May 2017.
    2. 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.
    3. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    10. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    11. 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).
    12. 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.
    13. Kouritzin, Michael A. & MacKay, Anne, 2018. "VIX-linked fees for GMWBs via explicit solution simulation methods," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 1-17.
    14. 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.
    15. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    16. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
    17. 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.
    18. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    19. 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.
    20. 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.

    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:gam:jrisks:v:6:y:2018:i:3:p:103-:d:170856. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.