Approximate hedging problem with transaction costs in stochastic volatility markets

Abstract

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.