IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1604.00105.html
   My bibliography  Save this paper

Option pricing under fast-varying long-memory stochastic volatility

Author

Listed:
  • Josselin Garnier
  • Knut Solna

Abstract

Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider European option pricing. This means that the volatility process is neither a Markov process nor a martingale. However, by exploiting the fact that the price process is still a semimartingale and accordingly using the martingale method, we can obtain an analytical expression for the option price in the regime where the volatility process is fast mean-reverting. The volatility process is modeled as a smooth and bounded function of a fractional Ornstein-Uhlenbeck process. We give the expression for the implied volatility, which has a fractional term structure.

Suggested Citation

  • Josselin Garnier & Knut Solna, 2016. "Option pricing under fast-varying long-memory stochastic volatility," Papers 1604.00105, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1604.00105
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1604.00105
    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. Cao, Jiling & Kim, Jeong-Hoon & Kim, See-Woo & Zhang, Wenjun, 2020. "Rough stochastic elasticity of variance and option pricing," Finance Research Letters, Elsevier, vol. 37(C).
    2. Anine E. Bolko & Kim Christensen & Mikko S. Pakkanen & Bezirgen Veliyev, 2020. "A GMM approach to estimate the roughness of stochastic volatility," Papers 2010.04610, arXiv.org, revised Apr 2022.
    3. Anine E. Bolko & Kim Christensen & Mikko S. Pakkanen & Bezirgen Veliyev, 2020. "Roughness in spot variance? A GMM approach for estimation of fractional log-normal stochastic volatility models using realized measures," CREATES Research Papers 2020-12, Department of Economics and Business Economics, Aarhus University.
    4. Benjamin James Duthie, 2019. "Portfolio optimisation under rough Heston models," Papers 1909.02972, arXiv.org.

    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:1604.00105. 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.