IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v26y2024i2d10.1007_s11009-024-10082-1.html
   My bibliography  Save this article

Conditional Moment Matching and Stratified Approximation for Pricing and Hedging Periodic-Premium Variable Annuities

Author

Listed:
  • Xiao Wei

    (Central University of Finance and Economics)

  • Xingchi Gu

    (Central University of Finance and Economics)

Abstract

This paper extends the stratified approximation method using lognormal and gamma distributions - first introduced to price Asian options - to derive a close formula for pricing and hedging of periodic-premium variable annuities. We used the moment matching method to fit the lognormal and gamma distributions to the conditional distribution of the integral of the underlying asset on a time interval, given the terminal value of the underlying asset. The highly oscillating double integrals for computing an expectation about the integral of the underlying assets are simplified down to a single integral, which greatly reduces the computation time for pricing periodic-premium variable annuities. This method allowed us to construct a different delta hedging strategy, other than the one used in the existing literature for embedded option of periodic-premium variable annuities. Compared with the existing research on pricing periodic-premium variable annuities, we obtained more accurate results using the stratified approximation method than the numerical method of partial differential equations, and found that the underpricing problem with periodic-premium variable annuities is even more severe than previously stated in existing literature. We further investigated the price gap between single-premium and periodic-premium variable annuities in a variety of settings, and examined the impact that the model and product parameters had on the price gap. The robustness and accuracy of the proposed method is tested by numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:2:d:10.1007_s11009-024-10082-1
    DOI: 10.1007/s11009-024-10082-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-024-10082-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-024-10082-1?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. 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.
    2. 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.
    3. 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.
    4. Privault, Nicolas & Wei, Xiao, 2018. "Fast Computation Of Risk Measures For Variable Annuities With Additional Earnings By Conditional Moment Matching," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 171-196, January.
    5. 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.
    6. Chi, Yichun & Lin, X. Sheldon, 2012. "Are Flexible Premium Variable Annuities Under-Priced?," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 559-574, November.
    7. 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.
    8. Carole Bernard & Zhenyu Cui & Steven Vanduffel, 2017. "Impact of Flexible Periodic Premiums on Variable Annuity Guarantees," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(1), pages 63-86, January.
    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. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
    2. 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.
    3. Moenig, Thorsten, 2021. "Variable annuities: Market incompleteness and policyholder behavior," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 63-78.
    4. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Seyed Amir Hejazi & Kenneth R. Jackson & Guojun Gan, 2017. "A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1701.04134, arXiv.org.
    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. 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).
    13. 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.
    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. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Bernard, Carole & Kwak, Minsuk, 2016. "Semi-static hedging of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 173-186.

    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:spr:metcap:v:26:y:2024:i:2:d:10.1007_s11009-024-10082-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.