Option markets can show you how the option price changes with a change in the strike price K. They can also show you how the price of an option moves with the spot price after the spot price has moved - however that isn't much use when you need to know before how much delta you need to trade to hedge. Most banks don't use simplistic models like BS to generate delta but more complicated models that incorporate vol surface dynamics as well based on assumptions they have around how the vol will behave with the spot move.