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arXiv · 2608.22620

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

Charles Clevenger·Xiang Wan
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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.

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BibTeXRIS

Charles Clevenger, Xiang Wan. 2026-08-23. WSVI: A Dimensionless Shape Family for Implied Volatility and Its Static No-Arbitrage Structure. https://arxiv.org/abs/2608.22620

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