Large-Maturity Regimes of the Heston Forward Smile

Stochastic Processes and Their Applications, 126: 1087-1123, 2016

30 Pages Posted: 29 Oct 2014 Last revised: 28 Mar 2016

See all articles by Antoine (Jack) Jacquier

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Patrick Roome

Imperial College London - Department of Mathematics

Date Written: October 27, 2014

Abstract

We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and different powers of the maturity come into play. As a by-product of the analysis we provide new implied volatility asymptotics, both in the forward case and in the spot case, as well as extended SVI-type formulae. The proofs are based on extensions and refinements of sharp large deviations theory, in particular in cases where standard convexity arguments fail.

Keywords: Stochastic volatility, Heston, forward implied volatility, asymptotic expansion, sharp large deviations.

JEL Classification: 60F10, 91G99, 91G60

Suggested Citation

Jacquier, Antoine and Roome, Patrick, Large-Maturity Regimes of the Heston Forward Smile (October 27, 2014). Stochastic Processes and Their Applications, 126: 1087-1123, 2016, Available at SSRN: https://ssrn.com/abstract=2515501 or http://dx.doi.org/10.2139/ssrn.2515501

Antoine Jacquier

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

Patrick Roome (Contact Author)

Imperial College London - Department of Mathematics ( email )

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

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