In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in Antonelli and Scarlatti, the expansion is done w.r.t. the correlation between the noises driving the underlying asset price process and the volatility process. We first obtain expressions for the power series' coefficients from the generalized Hull and White formula obtained in Al\`os. Afterwards, we provide representations turning out from the approach for the sensitivity problem tackled by Malliavin calculus techniques, and these allow to handle not only vanilla options. From a paper jointly written with Giorgio Ferrari and Roberta Piersimoni.