IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v13y2013i11p1813-1829.html
   My bibliography  Save this article

Fast Ninomiya--Victoir calibration of the double-mean-reverting model

Author

Listed:
  • Christian Bayer
  • Jim Gatheral
  • Morten Karlsmark

Abstract

We consider the three-factor double mean reverting (DMR) option pricing model of Gatheral [ Consistent Modelling of SPX and VIX Options , 2008], a model which can be successfully calibrated to both VIX options and SPX options simultaneously. One drawback of this model is that calibration may be slow because no closed form solution for European options exists. In this paper, we apply modified versions of the second-order Monte Carlo scheme of Ninomiya and Victoir [ Appl. Math. Finance , 2008, 15 , 107--121], and compare these to the Euler--Maruyama scheme with full truncation of Lord et al. [ Quant. Finance , 2010, 10 (2), 177--194], demonstrating on the one hand that fast calibration of the DMR model is practical, and on the other that suitably modified Ninomiya--Victoir schemes are applicable to the simulation of much more complicated time-homogeneous models than may have been thought previously.

Suggested Citation

  • Christian Bayer & Jim Gatheral & Morten Karlsmark, 2013. "Fast Ninomiya--Victoir calibration of the double-mean-reverting model," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1813-1829, November.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:11:p:1813-1829
    DOI: 10.1080/14697688.2013.818245
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2013.818245
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2013.818245?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 search for a different version of it.

    Citations

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


    Cited by:

    1. Andrew Papanicolaou, 2021. "Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options," Papers 2101.00299, arXiv.org, revised Mar 2021.
    2. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    3. Barletta, Andrea & Santucci de Magistris, Paolo & Violante, Francesco, 2019. "A non-structural investigation of VIX risk neutral density," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 1-20.
    4. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching stochastic volatility model: estimation and calibration to VIX options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(1), pages 38-75, January.
    5. Antoine Jacquier & Fangwei Shi, 2016. "The randomised Heston model," Papers 1608.07158, arXiv.org, revised Dec 2018.
    6. Zhiqiang Zhou & Wei Xu & Alexey Rubtsov, 2024. "Joint calibration of S&P 500 and VIX options under local stochastic volatility models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 273-310, January.
    7. Andrew Papanicolaou, 2018. "Consistent Time-Homogeneous Modeling of SPX and VIX Derivatives," Papers 1812.05859, arXiv.org, revised Mar 2022.
    8. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    9. Blanka Horvath & Oleg Reichmann, 2018. "Dirichlet Forms and Finite Element Methods for the SABR Model," Papers 1801.02719, arXiv.org.
    10. Andrew Papanicolaou & Ronnie Sircar, 2014. "A regime-switching Heston model for VIX and S&P 500 implied volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1811-1827, October.
    11. Jaegi Jeon & Geonwoo Kim & Jeonggyu Huh, 2021. "Consistent and efficient pricing of SPX and VIX options under multiscale stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 559-576, May.
    12. M. Avellaneda & A. Papanicolaou, 2019. "Statistics Of Vix Futures And Applications To Trading Volatility Exchange-Traded Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-30, February.
    13. Pacati, Claudio & Pompa, Gabriele & Renò, Roberto, 2018. "Smiling twice: The Heston++ model," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 185-206.
    14. Jaegi Jeon & Geonwoo Kim & Jeonggyu Huh, 2019. "Consistent and Efficient Pricing of SPX and VIX Options under Multiscale Stochastic Volatility," Papers 1909.10187, arXiv.org.
    15. Kim, See-Woo & Kim, Jeong-Hoon, 2018. "Analytic solutions for variance swaps with double-mean-reverting volatility," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 130-144.
    16. A. Papanicolaou, 2016. "Analysis of VIX Markets with a Time-Spread Portfolio," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 374-408, September.
    17. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 2016. "Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach," CREATES Research Papers 2016-20, Department of Economics and Business Economics, Aarhus University.
    18. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options," Working Papers hal-01212018, HAL.
    19. Andrew Papanicolaou, 2022. "Consistent time‐homogeneous modeling of SPX and VIX derivatives," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 907-940, July.

    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:taf:quantf:v:13:y:2013:i:11:p:1813-1829. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.