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Asymptotic formulae for implied volatility in the Heston model

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  • Martin Forde
  • Antoine Jacquier
  • Aleksandar Mijatovic

Abstract

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.

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File URL: http://arxiv.org/pdf/0911.2992
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0911.2992.

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Date of creation: Nov 2009
Date of revision: May 2010
Handle: RePEc:arx:papers:0911.2992

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Web page: http://arxiv.org/

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Cited by:
  1. Archil Gulisashvili & Josef Teichmann, 2014. "The G\"{a}rtner-Ellis theorem, homogenization, and affine processes," Papers 1406.3716, arXiv.org.
  2. Antoine Jacquier & Patrick Roome, 2013. "The Small-Maturity Heston Forward Smile," Papers 1303.4268, arXiv.org, revised Aug 2013.
  3. Zhi Guo & Eckhard Platen, 2011. "The Small and Large Time Implied Volatilities in the Minimal Market Model," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 297, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. P. Friz & S. Gerhold & A. Gulisashvili & S. Sturm, 2010. "On refined volatility smile expansion in the Heston model," Papers 1001.3003, arXiv.org, revised Nov 2010.
  5. Jim Gatheral & Antoine Jacquier, 2010. "Convergence of Heston to SVI," Papers 1002.3633, arXiv.org.
  6. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
  7. Archil Gulisashvili & Peter Laurence, 2013. "The Heston Riemannian distance function," Papers 1302.2337, arXiv.org.
  8. Forde, Martin, 2014. "The large-maturity smile for the Stein–Stein model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 91(C), pages 145-152.
  9. Antoine Jacquier & Aleksandar Mijatovic, 2012. "Large deviations for the extended Heston model: the large-time case," Papers 1203.5020, arXiv.org.
  10. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.

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