A Rough SABR Formula

Frontiers of Mathematical Finance, 2021

18 Pages Posted: 12 May 2021 Last revised: 30 Jun 2021

Date Written: May 11, 2021

Abstract

Following an approach originally suggested by Balland in the context of the SABR model, we derive an ODE that is satisfied by normalized volatility smiles for short maturities under a rough volatility extension of the SABR model that extends also the rough Bergomi model. We solve this ODE numerically and further present a very accurate approximation to the numerical solution that we dub the rough SABR formula.

Keywords: SABR, rough volatility, volatility surface

JEL Classification: G12, G13, C60, C63

Suggested Citation

Fukasawa, Masaaki and Gatheral, Jim, A Rough SABR Formula (May 11, 2021). Frontiers of Mathematical Finance, 2021, Available at SSRN: https://ssrn.com/abstract=3844278 or http://dx.doi.org/10.2139/ssrn.3844278

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

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