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

European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis