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
Date Written: January 27, 2018
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: 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
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