Asymptotic Formulae for Implied Volatility in the Heston Model

Proceedings of the Royal Society A

Posted: 16 Nov 2009 Last revised: 23 Mar 2012

See all articles by Martin Forde

Martin Forde

Dublin City University - Department of Mathematical Sciences

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Aleksandar Mijatovic

Imperial College London

Date Written: November 16, 2009

Abstract

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.

Keywords: implied volatility, Heston model, closed-form formula, saddlepoint approximation, calibration

JEL Classification: G12, G13, C6

Suggested Citation

Forde, Martin and Jacquier, Antoine and Mijatovic, Aleksandar, Asymptotic Formulae for Implied Volatility in the Heston Model (November 16, 2009). Proceedings of the Royal Society A, Available at SSRN: https://ssrn.com/abstract=1506930

Martin Forde

Dublin City University - Department of Mathematical Sciences ( email )

Dublin
Ireland

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/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Aleksandar Mijatovic

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/a.mijatovic

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