IDEAS home Printed from
   My bibliography  Save this paper

Arbitrage-free SVI volatility surfaces


  • Jim Gatheral
  • Antoine Jacquier


In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data.

Suggested Citation

  • Jim Gatheral & Antoine Jacquier, 2012. "Arbitrage-free SVI volatility surfaces," Papers 1204.0646,, revised Mar 2013.
  • Handle: RePEc:arx:papers:1204.0646

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
    5. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:kap:annfin:v:13:y:2017:i:1:d:10.1007_s10436-017-0292-1 is not listed on IDEAS
    2. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394,
    3. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020,, revised May 2017.
    4. Vinicius Albani & Uri M. Ascher & Jorge P. Zubelli, 2016. "Local Volatility Models in Commodity Markets and Online Calibration," Papers 1602.04372,
    5. Anastasis Kratsios & Cody B. Hyndman, 2017. "Arbitrage-Free Regularization," Papers 1710.05114,, revised Aug 2018.
    6. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    7. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500066 is not listed on IDEAS
    8. Thaddeus Neururer & George Papadakis & Edward J. Riedl, 2016. "Tests of investor learning models using earnings innovations and implied volatilities," Review of Accounting Studies, Springer, vol. 21(2), pages 400-437, June.
    9. Michael R. Tehranchi, 2017. "A Black--Scholes inequality: applications and generalisation," Papers 1701.03897,, revised Jan 2017.
    10. Stefano De Marco & Claude Martini, 2017. "Moment generating functions and Normalized implied volatilities: unification and extension via Fukasawa's pricing formula," Papers 1703.00957,, revised May 2017.
    11. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Extreme-Strike Asymptotics for General Gaussian Stochastic Volatility Models," Papers 1502.05442,, revised Feb 2017.
    12. Maarten Wyns & Jacques Du Toit, 2016. "A Finite Volume - Alternating Direction Implicit Approach for the Calibration of Stochastic Local Volatility Models," Papers 1611.02961,
    13. Antoine Jacquier & Claude Martini & Aitor Muguruza, 2017. "On VIX Futures in the rough Bergomi model," Papers 1701.04260,
    14. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    15. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2012. "Generalised arbitrage-free SVI volatility surfaces," Papers 1210.7111,, revised May 2016.
    16. repec:taf:quantf:v:18:y:2018:i:1:p:45-61 is not listed on IDEAS
    17. Pierre M. Blacque-Florentin & Badr Missaoui, 2015. "Nonparametric and arbitrage-free construction of call surfaces using l1-recovery," Papers 1506.06997,, revised Aug 2016.
    18. Samuel E. Vazquez, 2014. "Option Pricing, Historical Volatility and Tail Risks," Papers 1402.1255,
    19. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543,

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:1204.0646. 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: (arXiv administrators). General contact details of provider: .

    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.