Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs

Abstract

Local volatility models are popular as they can be calibrated to the market of European options by the simple Dupire formula. For such a model, we propose a modified Leland method which allows to approximately replicate a European contingent claim when the market is under proportional transaction costs. The convergence of the scheme is shown by means of a new strategy of proof based on partial differential equations (PDEs) techniques allowing us to obtain appropriate Greek estimations.

Key Words:

• Approximate hedging
• transaction costs
• local volatility
• Leland’s strategy

Acknowledgement

The authors thank the anonymous referees for constructive criticism and helpful suggestions which improved the presentation of the paper.