Convergence of Heston to SVI
AbstractIn this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a simpler expression for the asymptotic implied volatility in the Heston model. We show how this result can help in interpreting SVI parameters.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Quantitative Finance.
Volume (Year): 11 (2011)
Issue (Month): 8 ()
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Web page: http://www.tandfonline.com/RQUF20
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- Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
- Antoine Jacquier & Aleksandar Mijatovic, 2012. "Large deviations for the extended Heston model: the large-time case," Papers 1203.5020, arXiv.org.
- J. D. Deuschel & P. K. Friz & A. Jacquier & S. Violante, 2013. "Marginal density expansions for diffusions and stochastic volatility, part II: Applications [to the Stein--Stein model]," Papers 1305.6765, arXiv.org.
- J. D. Deuschel & P. K. Friz & A. Jacquier & S. Violante, 2011. "Marginal density expansions for diffusions and stochastic volatility, part I: Theoretical Foundations," Papers 1111.2462, arXiv.org, revised May 2013.
- Forde, Martin, 2014. "The large-maturity smile for the Stein–Stein model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 145-152.
- Jim Gatheral & Antoine Jacquier, 2012. "Arbitrage-free SVI volatility surfaces," Papers 1204.0646, arXiv.org, revised Mar 2013.
- Martin Forde & Antoine Jacquier, 2011. "The large-maturity smile for the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 755-780, December.
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