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Explicit no arbitrage domain for sub-SVIs via reparametrization

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  • Claude Martini
  • Arianna Mingone

Abstract

The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We study here the case of some sub-SVIs (all with 3 parameters): the Symmetric SVI, the Vanishing Upward/Downward SVI, and SSVI, for which we provide an explicit domain, with no numerical procedure required.

Suggested Citation

  • Claude Martini & Arianna Mingone, 2021. "Explicit no arbitrage domain for sub-SVIs via reparametrization," Papers 2106.02418, arXiv.org.
    • Handle: RePEc:arx:papers:2106.02418
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    File URL: http://arxiv.org/pdf/2106.02418
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    References listed on IDEAS

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    1. Michael R. Tehranchi, 2020. "A Black–Scholes inequality: applications and generalisations," Finance and Stochastics, Springer, vol. 24(1), pages 1-38, January.
    2. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    3. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2012. "Generalised arbitrage-free SVI volatility surfaces," Papers 1210.7111, arXiv.org, revised May 2016.
    4. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
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    Cited by:

    1. Claude Martini & Arianna Mingone, 2023. "Options are also options on options: how to smile with Black-Scholes," Papers 2308.04130, arXiv.org.
    2. Arianna Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Papers 2204.00312, arXiv.org.

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