Is there any way to calculate nifty option price exactly?

B&S formula has been used in arriving nifty option price, but it always gives theoretical value. But how does the practical value is arrived.

Why always there is a difference in option price calculators and real value ? Is there anyway to calculate the exact value of the option price ?

I’m here referring to only NIFTY options not in any stocks.

It doesn’t matter whether it is Nifty or BN or any other index or stock.
The price of option is determined by Bid/Ask or supply/demand.

But this raises another question(i don’t know the answer) that if option price is solely dependent on bid/ask, why does it follow the B&S formula and things like price going down at the expiry?