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WSVI: A Dimensionless Shape Family for Implied Volatility and Its Static No-Arbitrage Structure

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  • Charles Clevenger
  • Xiang Wan

Abstract

W-shaped smiles appear in near-expiry options around binary events such as earnings, and have been associated with bimodal risk-neutral densities. The three-parameter eSSVI slice cannot produce them. This paper defines WSVI, a parametric family for implied volatility that admits negative at-the-forward curvature and bimodal implied densities, and develops its static no-arbitrage structure. The construction factorizes total variance into a level and a dimensionless shape of normalized log-moneyness. The shape extends the per-slice eSSVI form with bounded one-sided basis terms, which add flexibility in the interior while leaving the leading-order wing behavior controlled by the affine and quadratic components. We characterize the family's exact domain and write the butterfly, vertical spread, and calendar conditions directly in shape coordinates.

Suggested Citation

  • Charles Clevenger & Xiang Wan, 2026. "WSVI: A Dimensionless Shape Family for Implied Volatility and Its Static No-Arbitrage Structure," Papers 2608.22620, arXiv.org.
    • Handle: RePEc:arx:papers:2608.22620
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    References listed on IDEAS

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    1. Paul Glasserman & Dan Pirjol, 2023. "W-shaped implied volatility curves and the Gaussian mixture model," Quantitative Finance, Taylor & Francis Journals, vol. 23(4), pages 557-577, April.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    4. Arianna Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Papers 2204.00312, arXiv.org.
    5. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    6. A. Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 22(12), pages 2205-2217, December.
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