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?

  • $\begingroup$ 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). $\endgroup$ – Alex C Jun 14 at 18:12
  • $\begingroup$ thank you. can we replicate the option if we hedge using the leland modified volatility and if the transaction costs are constant? $\endgroup$ – user40929 Jun 17 at 13:43
  • $\begingroup$ Perfect replication no, you will replicate with a (random) hedging error $\endgroup$ – Alex C Jun 17 at 15:42

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