Robust approach to pricing and hedging of contingent claims

Abstract: The classical approach in mathematical finance start with an a priori model in which prices and hedges are then computed. It fails to incorporate fully the information available in the markets, it usually describes frictionless trading and most importantly it tell us nothing of the situation when the reality departs from the prescribed model dynamics. These are important theoretical shortcomings. Practical inadequacy of the classical model-specific arguments has been exposed by the recent financial crisis.
In this work we set out to develop a robust alternative. We propose a coherent mathematical framework for pricing and hedging which starts with the information available in the market and does not make specific modelling assumptions. We discuss in more detail the example of pricing and hedging of double barrier options when the prices of co-maturing European calls and puts are available in the market. Finally, we compare numerically the performance of robust and classical hedging strategies in presence of model uncertainty and/or market frictions.