A decomposition formula for option prices in the Heston model and applications to option pricing approximation
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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.
KeywordsStochastic volatility Heston model Itô calculus
Mathematics Subject Classification91B28 91B70
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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