Recapitulating the history of Black-Scholes:
- Nobody knows the fair price of options.
- Revolution: BS! You put in all the parameters and get a price -> A Nobel Prize for that one!
- Wait: Nobody knows the true value of future volatility, so we cannot calculate the fair price after all and are back to square one.
- But ok: Assuming Mr. Market is always right we now have it backwards: putting in real market prices of options and calculating their implied volatility via BS.
So what we are basically doing is exchanging the uncertainty about the fair price of an option for the uncertainty about future volatility - or just a mathematically sophisticated transformation of uncertainty per se. We could have had the "Mr. Market is always right"-thing without the complex mathematical machinery, couldn't we?
I know, one of the accomplishments of BS is that the option price is independent of any drift of the underlying but still my question is:
Is my short characterisation above correct and if yes, how does it really help to transform one form of uncertainty into another and still not be able to calculate a fair price (why you started the whole endeavour in the first place)?