IDEAS home Printed from https://ideas.repec.org/a/bpj/apjrin/v10y2016i2p133-153n1.html

Pricing of Guaranteed Annuity Options in a Stochastic Volatility and Interest Rate Environment

Author

Listed:
  • Kizaki Keisuke

    (Graduate School of Economics and Management, Tohoku University, 27–1 Kawauchi, Aoba-Ku, Sendai City 980–8576, Japan)

  • Muroi Yoshifumi

    (Graduate School of Economics and Management, Tohoku University, 27–1 Kawauchi, Aoba-Ku, Sendai City 980–8576, Japan)

Abstract

This article examines the pricing of guaranteed annuity options (GAOs) in a stochastic volatility and interest rate model. While the pricing of these options in a stochastic volatility and interest rate model has been examined in van Haastrecht, Plat, and Pelsser (2010. Insurance: Mathematics and Economics 47:266–77), the pricing is difficult under the general stochastic volatility environment. In order to overcome these difficulties, we examined the asymptotic expansion method introduced by Kim and Kunitomo (1999. Asia-Pacific Financial Markets 6:49–70) and extended by Kim (2002. Journal of the Operations Research Society of Japan 45:404–25), and Kunitomo and Kim (2007. Japanese Economic Review 58:71–106). The asymptotic expansion method obtains a closed-form approximation formula for the price of GAOs in a general stochastic volatility environment including the Schöbel–Zhu–Hull–White model and the Heston–Hull–White model, for example. We confirm the accuracy of the asymptotic expansion methods by numerical demonstrations. The sensitivity analysis of the options price to changes in the parameters for the stochastic volatility process is also analyzed.

Suggested Citation

  • Kizaki Keisuke & Muroi Yoshifumi, 2016. "Pricing of Guaranteed Annuity Options in a Stochastic Volatility and Interest Rate Environment," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 10(2), pages 133-153, July.
    • Handle: RePEc:bpj:apjrin:v:10:y:2016:i:2:p:133-153:n:1
    DOI: 10.1515/apjri-2015-0013
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/apjri-2015-0013
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/apjri-2015-0013?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    2. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
    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. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019, January-A.

    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. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    2. Ruan, Xinfeng & Zhang, Jin E., 2021. "The economics of the financial market for volatility trading," Journal of Financial Markets, Elsevier, vol. 52(C).
    3. Yun, Jaeho, 2014. "Out-of-sample density forecasts with affine jump diffusion models," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 74-87.
    4. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    5. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    6. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    7. Juho Kanniainen & Martin Magris, 2018. "Option market (in)efficiency and implied volatility dynamics after return jumps," Papers 1810.12200, arXiv.org.
    8. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming & Tenyakov, Anton, 2015. "Mortality modelling with regime-switching for the valuation of a guaranteed annuity option," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 108-120.
    9. Chernov, Mikhail & Graveline, Jeremy & Zviadadze, Irina, 2018. "Crash Risk in Currency Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(1), pages 137-170, February.
    10. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    11. Valeria D’Amato & Emilia Di Lorenzo & Steven Haberman & Maria Russolillo & Marilena Sibillo, 2011. "The Poisson Log-Bilinear Lee-Carter Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 315-333.
    12. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    13. Samuel Tabot Enow, 2025. "Exploring stochastic volatility in financial market," International Journal of Research in Business and Social Science (2147-4478), Center for the Strategic Studies in Business and Finance, vol. 14(1), pages 74-79, January.
    14. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    15. Sonali Jain & Jayanth R. Varma & Sobhesh Kumar Agarwalla, 2019. "Indian equity options: Smile, risk premiums, and efficiency," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 150-163, February.
    16. Masahiro Watanabe, 2003. "A Model of Stochastic Liquidity," Yale School of Management Working Papers ysm385, Yale School of Management.
    17. van Haastrecht, Alexander & Plat, Richard & Pelsser, Antoon, 2010. "Valuation of guaranteed annuity options using a stochastic volatility model for equity prices," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 266-277, December.
    18. Fan, Chenxi & Luo, Xingguo & Wu, Qingbiao, 2017. "Stochastic volatility vs. jump diffusions: Evidence from the Chinese convertible bond market," International Review of Economics & Finance, Elsevier, vol. 49(C), pages 1-16.
    19. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
    20. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:bpj:apjrin:v:10:y:2016:i:2:p:133-153:n: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: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.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.