transactions costs and leland modified volatility

When there are transactions costs, we are in a situation of incomplete market. What does the modified volatility of Leland (Option Pricing and Replication with Transactions Costs, 1985) bring us? can we replicate the option when computing/hedging the risks with this volatility?

• Once you select a hedging frequency, dynamic hedging at that frequency using the Leland modified vol is certainly a feasible strategy, but it is not necessarily optimal. (In particular as $\Delta t$ becomes small it is probably not an optimal strategy, and not in continuous time limit). Still, it provides a useful estimate of option value in practical cases, where hedging is discrete time (and assuming you are selling and then hedging the option). – Alex C Jun 14 at 18:12
• thank you. can we replicate the option if we hedge using the leland modified volatility and if the transaction costs are constant? – user40929 Jun 17 at 13:43
• Perfect replication no, you will replicate with a (random) hedging error – Alex C Jun 17 at 15:42