Understanding Short-Term Implied Volatility Dynamics: A Model-Independent Approach Beyond Stochastic Volatility

Abstract: This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely concerned in the option market. Departing from conventional process-based models that rely on explicit stochastic differential equations, our work adopts a model-independent, distribution-based approach by imposing cumulant conditions on the asset's log return distribution. Under these broad assumptions, we derive a quadratic expansion for the implied volatility as a function of moneyness for near-the-money options, along with asymptotic expressions for the ATM skew and curvature as the time to maturity tends to zero. These results not only highlight the differences in the properties of ATM asymptotics among different types of models, but also offer a versatile framework for model calibration, including regular stochastic volatility, rough volatility, and discrete-time distribution-based models, using simple moment information. Overall, our findings provide robust analytical tools for the accurate approximation of short-term option prices and the evaluation of model performance against market stylized features.