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Robust calibration and arbitrage-free interpolation of SSVI slices

Author

Listed:
  • Jacopo Corbetta

    (Zeliade Systems)

  • Pierre Cohort

    (Zeliade Systems)

  • Ismail Laachir

    (Zeliade Systems)

  • Claude Martini

    (Zeliade Systems)

Abstract

We describe a robust calibration algorithm of a set of SSVI maturity slices (i.e., a set of 3 SSVI parameters $$\theta _t, \rho _t, \varphi _t$$θt,ρt,φt attached to each option maturity t available on the market), which grants that these slices are free of butterfly and of calendar spread arbitrage. Given such a set of consistent SSVI parameters, we show that the most natural interpolation/extrapolation of the parameters provides a full continuous volatility surface free of arbitrage. The numerical implementation is straightforward, robust and quick, yielding an effective and parsimonious solution to the smile problem, which has the potential to become a benchmark one. We thank Antoine Jacquier and Stefano De Marco for useful discussions and remarks. All remaining errors are ours.

Suggested Citation

  • Jacopo Corbetta & Pierre Cohort & Ismail Laachir & Claude Martini, 2019. "Robust calibration and arbitrage-free interpolation of SSVI slices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 665-677, December.
    • Handle: RePEc:spr:decfin:v:42:y:2019:i:2:d:10.1007_s10203-019-00249-8
    DOI: 10.1007/s10203-019-00249-8
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    References listed on IDEAS

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    1. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
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    Cited by:

    1. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    2. Mehdi El Amrani & Antoine Jacquier & Claude Martini, 2019. "Dynamics of symmetric SSVI smiles and implied volatility bubbles," Papers 1909.10272, arXiv.org, revised Feb 2021.
    3. Claude Martini & Arianna Mingone, 2020. "No arbitrage SVI," Papers 2005.03340, arXiv.org, revised May 2021.

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