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Generalized Arbitrage-Free SVI Volatility Surfaces

Author

Listed:
  • Gaoyue Guo

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Antoine Jacquier

    (Imperial College London)

  • Claude Martini

    (Zeliade Systems)

  • Leo Neufcourt

    (Columbia University [New York])

Abstract

In this article we propose a generalisation of the recent work of Gatheral and Jacquier on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper. We further exhibit an arbitrage-free volatility surface different from Gatheral's SVI parameterisation.

Suggested Citation

  • Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2016. "Generalized Arbitrage-Free SVI Volatility Surfaces," Post-Print hal-05564337, HAL.
    • Handle: RePEc:hal:journl:hal-05564337
    DOI: 10.1137/120900320
    Note: View the original document on HAL open archive server: https://hal.science/hal-05564337v1
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    References listed on IDEAS

    as
    1. Antoine Jacquier & Martin Keller-Ressel, 2015. "Implied volatility in strict local martingale models," Papers 1508.04351, arXiv.org.
    2. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    3. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
    4. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    5. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
    6. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    7. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12, January.
    8. L. Rogers & M. Tehranchi, 2010. "Can the implied volatility surface move by parallel shifts?," Finance and Stochastics, Springer, vol. 14(2), pages 235-248, April.
    9. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
    10. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
    11. David Hobson, 2010. "Comparison results for stochastic volatility models via coupling," Finance and Stochastics, Springer, vol. 14(1), pages 129-152, January.
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    Cited by:

    1. Martin Keller-Ressel & Hannes Nikulski, 2026. "Discovering parametrizations of implied volatility with symbolic regression," Papers 2603.21892, arXiv.org.
    2. Claude Martini & Arianna Mingone, 2020. "No arbitrage SVI," Papers 2005.03340, arXiv.org, revised May 2021.
    3. Dilip B. Madan & Wim Schoutens, 2019. "Arbitrage Free Approximations to Candidate Volatility Surface Quotations," JRFM, MDPI, vol. 12(2), pages 1-21, April.

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