Short-Term at-the-Money Asymptotics Under Stochastic Volatility Models

SIAM Journal on Financial Mathematics, Vol. 10, No. 2, 491-511, 2019

20 Pages Posted: 5 Feb 2018 Last revised: 12 Jun 2019

See all articles by Omar El Euch

Omar El Euch

Ecole Polytechnique, Paris

Masaaki Fukasawa

Osaka University

Jim Gatheral

CUNY Baruch College

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau

Date Written: January 27, 2018

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.

Suggested Citation

El Euch, Omar and Fukasawa, Masaaki and Gatheral, Jim and Rosenbaum, Mathieu, Short-Term at-the-Money Asymptotics Under Stochastic Volatility Models (January 27, 2018). SIAM Journal on Financial Mathematics, Vol. 10, No. 2, 491-511, 2019. Available at SSRN: https://ssrn.com/abstract=3111471 or http://dx.doi.org/10.2139/ssrn.3111471

Omar El Euch

Ecole Polytechnique, Paris ( email )

1 rue Descartes
Paris, 75005
France

Masaaki Fukasawa

Osaka University

1-1 Yamadaoka
Suita
Osaka, 565-0871
Japan

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

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