Short-term at-the-money asymptotics under stochastic volatility models

TL;DR

This paper derives small-time asymptotic expansions for asset prices and implied volatilities under stochastic volatility models, providing insights into the behavior of at-the-money options and implied volatility surface features.

Contribution

It introduces a general small-time Edgeworth expansion for asset price densities and applies it to derive asymptotics for implied volatility skew and curvature, including the rough Bergomi model.

Findings

Asymptotic formulas for at-the-money implied volatility and skew

Limit theorem for implied volatility curvature

Application to the rough Bergomi model

Abstract

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary. The rough Bergomi model is treated as an example.