A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatility framework can be decomposed in the sum of four terms, which identify the main features of the market that affect to option prices: the expected future volatility, the correlation between the volatility and the noise driving the stock prices, the market price of volatility risk and the difference of the expected future volatility at different times. We also study some applications of this decomposition.