Short-Term Asymptotics of Volatility Skew and Curvature Based on Cumulants

Liexin Cheng and Xue Cheng

Papers from arXiv.org

Abstract: We introduce a novel cumulant-based method for approximating the shape of implied volatility smiles, applicable to the widely-used stochastic volatility models and distribution-based asset pricing models. We adopt an Edgeworth expansion technique to study the at-the-money (ATM) skew and curvature of the implied volatility surface. We propose cumulant conditions to derive their short-term asymptotics. Then we show that the conditions are satisfied by a wide scope of regular stochastic volatility models, rough volatility models and distribution-based models.

Date: 2024-01, Revised 2025-03
New Economics Papers: this item is included in nep-rmg
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