Large deviations for the extended Heston model: the large-time case
AbstractWe study here the large-time behaviour 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 behaviours of the asymptotic smile. In particular, we show that the condition assumed in Gatheral and Jacquier under which the Heston implied volatility converges to the SVI parameterisation is necessary and sufficient.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1203.5020.
Date of creation: Mar 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-03 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Martin Forde & Antoine Jacquier, 2011. "The large-maturity smile for the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 755-780, December.
- Jim Gatheral & Antoine Jacquier, 2011.
"Convergence of Heston to SVI,"
Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
- Agnieszka Janek & Tino Kluge & Rafał Weron & Uwe Wystup, 2010.
"FX Smile in the Heston Model,"
SFB 649 Discussion Papers
SFB649DP2010-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Janek, Agnieszka & Kluge, Tino & Weron, Rafal & Wystup, Uwe, 2010. "FX Smile in the Heston Model," MPRA Paper 25491, University Library of Munich, Germany.
- Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," Papers 1010.1617, arXiv.org.
- Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
- Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78.
- Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
- Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
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