IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01697117.html
   My bibliography  Save this paper

Multi-factor approximation of rough volatility models

Author

Listed:
  • Eduardo Abi Jaber

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

  • Omar El Euch

    () (X - École polytechnique)

Abstract

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting.

Suggested Citation

  • Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
  • Handle: RePEc:hal:journl:hal-01697117
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01697117v3
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-01697117v3/document
    Download Restriction: no

    References listed on IDEAS

    as
    1. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    2. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    3. Omar El Euch & Mathieu Rosenbaum, 2017. "Perfect hedging in rough Heston models," Papers 1703.05049, arXiv.org.
    4. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    5. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    6. Philippe Carmona & Laure Coutin & G. Montseny, 2000. "Approximation of Some Gaussian Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 161-171, January.
    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. Aditi Dandapani & Paul Jusselin & Mathieu Rosenbaum, 2019. "From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect," Papers 1907.06151, arXiv.org.

    More about this item

    Keywords

    limit theorems; affine Volterra processes; Rough volatility models; rough Heston models; stochastic Volterra equations; fractional Riccati equations;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:hal-01697117. 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: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.