Arbitrage-Free SVI Volatility Surfaces

Quantitative Finance, Vol. 14, No. 1, 59-71, 2014.

27 Pages Posted: 3 Apr 2012 Last revised: 15 Jan 2014

Jim Gatheral

CUNY Baruch College

Antoine Jacquier

Imperial College London

Date Written: March 17, 2013

Abstract

In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data.

Keywords: implied volatility, volatility surface, arbitrage-free parameterization, SVI, calibration

JEL Classification: G12, G13, C60, C63

Suggested Citation

Gatheral, Jim and Jacquier, Antoine, Arbitrage-Free SVI Volatility Surfaces (March 17, 2013). Quantitative Finance, Vol. 14, No. 1, 59-71, 2014.. Available at SSRN: https://ssrn.com/abstract=2033323 or http://dx.doi.org/10.2139/ssrn.2033323

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

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

Antoine Jacquier

Imperial College London ( email )

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

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

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