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, http://ssrn.com/abstract=1459662) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.