  This paper studies the problem of option replication in general stochastic
volatility markets with transaction costs, using a new specification for the
volatility adjustment in Leland's algorithm \cite{Leland}. We prove several
limit theorems for the normalized replication error of Leland's strategy, as
well as that of the strategy suggested by L\'epinette. The asymptotic results
obtained not only generalize the existing results, but also enable us to fix
the under-hedging property pointed out by Kabanov and Safarian. We also discuss
possible methods to improve the convergence rate and to reduce the option price
inclusive of transaction costs.
