Beyond the Leland strategies

Abstract: In the Black and Scholes model with proportional transaction costs, the Leland strategy allows to asymptotically super-replicate the European Call option as the number of revision dates converges to + infinity and the transaction costs rate tends rapidly to 0. This method relies heavily on the explicit expression of the delta-hedging strategy in the Black and Scholes model where the volatility is enlarged to compensate for the transaction costs. We solve the same problem of super-hedging but for a general model with an arbitrary fixed number of revision dates and arbitrary fixed transaction costs rates. Moreover, our approach does not need the existence of a risk-neutral probability measure and is (almost) model free and easily implementable from real data.