IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions

Listed author(s):
  • Yang, Sharon S.
  • Dai, Tian-Shyr
Registered author(s):

    Valuing guaranteed minimum withdrawal benefit (GMWB) has attracted significant attention from both the academic field and real world financial markets. However, some popular provisions of GMWB contracts, like the deferred life annuity structure, rollup interest rate guarantees, and surrender options are hard to be evaluated analytically and are rarely addressed in the academic literature. This paper proposes a flexible tree model that can accurately evaluate the values and the fair insurance fees of GMWBs. The flexibility of our tree allows us to faithfully implement the aforementioned provisions without introducing significant numerical pricing errors. The mortality risk can also be easily incorporated into our pricing model. Our numerical results verify the robustness of our tree and demonstrate how the aforementioned provisions and the mortality risk significantly influence the values and the fair insurance fees of GMWBs.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712001710
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 52 (2013)
    Issue (Month): 2 ()
    Pages: 231-242

    as
    in new window

    Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:231-242
    DOI: 10.1016/j.insmatheco.2012.12.005
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as
    in new window


    1. Boyle, Phelim & Hardy, Mary, 2003. "Guaranteed Annuity Options," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(02), pages 125-152, November.
    2. Ledlie, M. C. & Corry, D. P. & Finkelstein, G. S. & Ritchie, A. J. & Su, K. & Wilson, D. C. E., 2008. "Variable Annuities," British Actuarial Journal, Cambridge University Press, vol. 14(02), pages 327-389, July.
    3. 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.
    4. 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.
    5. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    6. Costabile, Massimo & Massab├│, 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.
    7. 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.
    8. Brennan, Michael J & Schwartz, Eduardo S, 1979. "Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance Policies with an Asset Value Guarantee," The Journal of Business, University of Chicago Press, vol. 52(1), pages 63-93, January.
    9. Michel Denuit & Pierre Devolder & Anne-C├ęcile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113.
    10. Christopher M Condron, 2008. "Variable Annuities and the New Retirement Realities*," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 33(1), pages 12-32, January.
    11. 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.
    12. Kijima, Masaaki, 2006. "A Multivariate Extension of Equilibrium Pricing Transforms: The Multivariate Esscher and Wang Transforms for Pricing Financial and Insurance Risks," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(01), pages 269-283, May.
    13. 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.
    14. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    15. 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.
    16. 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.
    17. 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.
    18. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
    19. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 621-651, November.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:231-242. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.