IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0911.2992.html
   My bibliography  Save this paper

Asymptotic formulae for implied volatility in the Heston model

Author

Listed:
  • Martin Forde
  • Antoine Jacquier
  • Aleksandar Mijatovic

Abstract

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.

Suggested Citation

  • Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
    • Handle: RePEc:arx:papers:0911.2992
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0911.2992
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    2. Yan, Shuang & Gu, Changgui & Yang, Huijie, 2024. "Bridge successive states for a complex system with evolutionary matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    3. Antoine Jacquier & Aleksandar Mijatović, 2014. "Large Deviations for the Extended Heston Model: The Large-Time Case," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 263-280, September.
    4. Zhi Jun Guo & Eckhard Platen, 2012. "The Small And Large Time Implied Volatilities In The Minimal Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-23.
    5. Martin Forde & Antoine Jacquier, 2011. "The large-maturity smile for the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 755-780, December.
    6. Forde, Martin, 2014. "The large-maturity smile for the Stein–Stein model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 145-152.
    7. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    8. Florence Guillaume & Wim Schoutens, 2014. "Heston Model: The Variance Swap Calibration," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 76-89, April.
    9. Antoine Jacquier & Fangwei Shi, 2016. "The randomised Heston model," Papers 1608.07158, arXiv.org, revised Dec 2018.
    10. Archil Gulisashvili & Peter Laurence, 2013. "The Heston Riemannian distance function," Papers 1302.2337, arXiv.org.
    11. P. Friz & S. Gerhold & A. Gulisashvili & S. Sturm, 2010. "On refined volatility smile expansion in the Heston model," Papers 1001.3003, arXiv.org, revised Nov 2010.
    12. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256, arXiv.org, revised Mar 2016.
    13. Shuaiqiang Liu & Anastasia Borovykh & Lech A. Grzelak & Cornelis W. Oosterlee, 2019. "A neural network-based framework for financial model calibration," Papers 1904.10523, arXiv.org.
    14. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
    15. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    16. Archil Gulisashvili & Josef Teichmann, 2014. "The G\"{a}rtner-Ellis theorem, homogenization, and affine processes," Papers 1406.3716, arXiv.org.
    17. S. T. Tse & Justin W. L. Wan, 2013. "Low-bias simulation scheme for the Heston model by Inverse Gaussian approximation," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 919-937, May.
    18. Shuzhen Yang & Wenqing Zhang, 2023. "Fixed-point iterative algorithm for SVI model," Papers 2301.07830, arXiv.org.
    19. Antoine Jacquier & Patrick Roome, 2013. "The Small-Maturity Heston Forward Smile," Papers 1303.4268, arXiv.org, revised Aug 2013.

    More about this item

    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:arx:papers:0911.2992. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.