Hedging problem for the Asian call options with transaction costs

In this paper, we develop asymptotic Asian option hedging methods for the Black–Scholes markets with transaction costs. We first construct classical replication strategies and then, using the Leland approach, propose corresponding modifications for the financial markets with proportional transaction costs. Sufficient conditions are found on the transaction costs implying the asymptotic hedging for the constructed strategies. The pricing problem is also considered. Three cases are studied: the case where the option price is the same as for the hedging problem without transaction costs, the case of increasing volatility, and the case where the option price equals the option price of the “buy and hold” strategy for European call options.