Large Deviations for the Extended Heston Model: The Large-Time Case

21 Pages Posted: 24 Mar 2012

See all articles by Antoine (Jack) Jacquier

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Aleksandar Mijatovic

Imperial College London

Date Written: March 22, 2012

Abstract

We study here the large-time behavior of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals pathological behaviors of the asymptotic smile. In particular, we show that the condition assumed in Gatheral & Jacquier (GJ10) under which the Heston implied volatility converges to the SVI parameterization is necessary and sufficient.

Keywords: Heston, large maturity, asymptotics, large deviations

JEL Classification: G12, G13, C60, C63

Suggested Citation

Jacquier, Antoine and Mijatovic, Aleksandar, Large Deviations for the Extended Heston Model: The Large-Time Case (March 22, 2012). Available at SSRN: https://ssrn.com/abstract=2027548 or http://dx.doi.org/10.2139/ssrn.2027548

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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