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

2026-08-23

AI Summary

本文定义了WSVI模型，解决了eSSVI无法生成W形波动率微笑的问题，并开发了其静态无套利结构。

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.

Problem

• W-shaped smiles
• bimodal risk-neutral densities
• negative at-the-forward curvature

Innovation

• WSVI
• negative at-the-forward curvature
• bimodal implied densities
• dimensionless shape
• no-arbitrage structure