Finance and Stochastics

, Volume 16, Issue 3, pp 403–422 | Cite as

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

  • Elisa AlòsEmail author


By means of classical Itô calculus, we decompose option prices as the sum of the classical Black–Scholes formula, with volatility parameter equal to the root-mean-square future average volatility, plus a term due to correlation and a term due to the volatility of the volatility. This decomposition allows us to develop first- and second-order approximation formulas for option prices and implied volatilities in the Heston volatility framework, as well as to study their accuracy for short maturities. Numerical examples are given.


Stochastic volatility Heston model Itô calculus 

Mathematics Subject Classification

91B28 91B70 

JEL Classification




A previous version of this paper has benefited from helpful comments by two anonymous referees.The author also wants to thank Prof. Vlad Bally for fruitful discussions and suggestions.

Supported by grants MTM2009-08869, Ministerio de Ciencia e Innovación and FEDER and SEJ2006-13537.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Dpt. d’Economia i EmpresaUniversitat Pompeu FabraBarcelonaSpain

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