I always wondered why the Black-Sholes-Merton model was used to estimate the price of European-style options when their prices are available on quoted exchanges?
I think I am missing something big here so any help would be great!
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The market price tells you what price you can currently buy/sell based on supply and demand. The Black-Scholes model is one way of estimating the fair market value. If they don't agree, then you may conclude that it's a good time to buy or sell.
Part of the reason is that OTC (over the counter) options aren't publicly quoted (obviously). Another part is that the implied volatility on the option is not a measurable input to the BSM model but is the volatility used in hedging a portfolio by minimizing volatility.