Let's say you want to find the fair price of a call option. One way is to use the black scholes formula. This assumes you can delta-hedge the underlying asset and the option to eliminate risk, and hence come up with a fair price such that there are theoretically no arbitrage opportunities.
However, what if you were NOT allowed to delta hedge? For example, what if the call option was bought over the counter (off exchange). Does the rationale of the black scholes option price still hold?