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

Omar El Euch; Masaaki Fukasawa; Jim Gatheral; Mathieu Rosenbaum

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arXiv · 1801.08675

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

Omar El Euch·Masaaki Fukasawa·Jim Gatheral·Mathieu Rosenbaum

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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.

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Omar El Euch, Masaaki Fukasawa, Jim Gatheral, Mathieu Rosenbaum. 2018-01-26. Short-term at-the-money asymptotics under stochastic volatility models. https://arxiv.org/abs/1801.08675

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