Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs

Abstract

Local volatility models are popular because they can be simply calibrated to the market of European options. For such models, we propose a modified Leland method which allows us to approximately replicate a European contingent claim when the market is under proportional transaction costs. The convergence of our scheme is shown by means of a new strategy of proof based on PDEs techniques allowing us to obtain appropriate Greeks estimations.