Convergence of Heston to SVI

Quantitative Finance, Vol. 11, No. 8, pp. 1129-1132, 2011

5 Pages Posted: 19 Feb 2010 Last revised: 31 Jul 2011

Date Written: February 18, 2010

Abstract

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a simpler expression for the asymptotic implied volatility in the Heston model. We show how this result can help in interpreting SVI parameters.

Keywords: SVI, Heston, Implied Volatility, Asymptotics, Calibration

JEL Classification: G12, G13, C60, C63

Suggested Citation

Gatheral, Jim and Jacquier, Antoine, Convergence of Heston to SVI (February 18, 2010). Quantitative Finance, Vol. 11, No. 8, pp. 1129-1132, 2011. Available at SSRN: https://ssrn.com/abstract=1555251

Jim Gatheral

CUNY Baruch College ( email )

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

Antoine Jacquier (Contact Author)

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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