# Intuitive understanding of Black-Scholes pricing

The Black-Scholes formula entails market completeness, so the price of an option is only the cost associated with dynamically hedging the option.

Where does this cost come from? I don't see how sustaining a replicating portfolio in a frictionless market can cost anything.

-
The instruments you use for the dynamic hedge cost money. –  Bob Jansen Jun 14 at 15:09

From a mathematical point of vue, your mistake comes from assuming that any martingale (like the actualized value of a self-financing portfolio $\widetilde{\Pi}_t := e^{-\int_0^t r_s ds} \Pi_t$, for $t\leq T$, under the risk neutral probability) has zero expected value when actually it just has constant expectated value. So if $\Pi$ is a replicating portfolio, the value of your derivative is equal to $\Pi_0$ and it can be non zero.