A number of futures contracts conveys to the short position various delivery options regarding the quality and exact timing of delivery. Moreover, the compensation to the long position is not solely determined by the market value of the delivered asset at the time of delivery. Sometimes, the long position can hedge this delivery risk by holding an appropriate portfolio of the underlying asset. It often has been stated that whenever the long position can form a dynamic hedge against the delivery risk, the delivery option has a zero value. This paper demonstrates the implication of such erroneous intuition to the pricing of options. It is shown that the root of the issue is the property of diffusion processes whereas, within a given time interval, a random variable either will never cross a given boundary or else, cross it an infinite number of times.