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

By means of classical It? calculus, we decompose option prices as the sum of the classical Black?CScholes 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.