  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 a recent paper by 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 by Elisa 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.
Finally, we show the numerical performance of the associated Monte Carlo
estimators for several stochastic volatility models.
