Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics

15 Pages Posted: 13 Feb 2015 Last revised: 29 Nov 2016

See all articles by Archil Gulisashvili

Archil Gulisashvili

Ohio University

Blanka Horvath

ETH Zürich - Department of Mathematics

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Date Written: November 22, 2016


We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable expressions, in particular when time becomes small or large. As an application -- in fact the original motivation for this paper -- we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by de finition arbitrage free, allow us to quantify the impact of the mass at zero on existing implied volatility approximations, and in particular how correct/erroneous these approximations become.

Keywords: SABR model, asymptotic expansions, implied volatility

JEL Classification: C5, C6

Suggested Citation

Gulisashvili, Archil and Horvath, Blanka and Jacquier, Antoine, Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics (November 22, 2016). Available at SSRN: or

Archil Gulisashvili

Ohio University ( email )

Athens, OH 45701-2979
United States
740-593-1281 (Phone)
740-593-9805 (Fax)

Blanka Horvath (Contact Author)

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092

Antoine Jacquier

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom


The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

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