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


Antoine Jacquier


Imperial College London - Department of Mathematics

Aleksandar Mijatovic


Imperial College London

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.

Number of Pages in PDF File: 21

Keywords: Heston, large maturity, asymptotics, large deviations

JEL Classification: G12, G13, C60, C63

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Date posted: March 24, 2012  

Suggested Citation

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

Contact Information

Antoine Jacquier (Contact Author)
Imperial College London - Department of Mathematics ( email )
South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
HOME PAGE: http://www.ma.ic.ac.uk/~ajacquie
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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