A model-free approach to delta hedging

Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a “risk-free” management. We utilize the existence of trends for financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton setting. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps. Keywords—Delta hedging, trends, quick fluctuations, abrupt changes, jumps, tracking control, model-free control. in ria -0 04 57 22 2, v er si on 1 16 F eb 2 01 0