  We obtain a decomposition of the call option price for a very general
stochastic volatility diffusion model extending the decomposition obtained by
E. Al\`os in [2] for the Heston model. We realize that a new term arises when
the stock price does not follow an exponential model. The techniques used are
non anticipative. In particular, we see also that equivalent results can be
obtained using Functional It\^o Calculus. Using the same generalizing ideas we
also extend to non exponential models the alternative call option price
decompostion formula obtained in [1] and [3] written in terms of the Malliavin
derivative of the volatility process. Finally, we give a general expression for
the derivative of the implied volatility under both, the anticipative and the
non anticipative case.
