We study the minimal initial capital needed to super-replicate an European contingent claim in the Black-Scholes model in the following `real' context: the hedger of the option will only trade at stopping times (which he may freely choose as the hedge ratios). In case the number of trading dates is fixed, we show that this capital corresponds to the buy-and-hold strategy (for a Call option, or the corresponding strategy for any option with a continuous payoff). In case the number may depend on the path of the underlying, we show that if the Black-Scholes delta of the contingent claim is itself a finite-variation process (which excludes standard options in general), this initial capital is the Black-Scholes price of the option. In other cases, e.g. standard options, even for the Call option, the question remains open
