  In this paper the valuation problem of a European call option in presence of
both stochastic volatility and transaction costs is considered. In the limit of
small transaction costs and fast mean reversion, an asymptotic expression for
the option price is obtained. While the dominant term in the expansion it is
shown to be the classical Black and Scholes solution, the correction terms
appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging
strategy is then explicitly obtained for the Scott's model.
