I cannot believe how completely clueless you are. It's not an implied distribution via the mkt price of the option unless you're ATM perfected with a strike = forward at 0.5 delta and using a straddle/sigma approximation, but that's not what you're referring to. This from a guy who doesn't know where the ETF divs come from. Implied vol is solved by using the market price of the option. That's it. I'm not going to respond. You get mated in six moves, shit on the board and declare victory.
If you listen to actual floor-traders like Taleb who got involved heavily into options as soon as they became listed, they'll tell you that the markets were pretty damn good at arriving at the correct pricing for them long before BSM came to the scene. In fact, when people finally did use the BSM model, it wasn't the vanilla algorithm, but one where traders did their own adjustments to it, since it only works on a fictional theory.
Huh, most OMMs in the day were automatics with delta sheets with a vol-shift. Upside calls were skewed before the '87 crash but not modeled (beyond vol corr). The first part of your post makes sense.
Funny, indeed. But price is observable at t, while (expected) future volatility can only be observed in a period t, t+1 So what you could do in your google sheets is calculating the ‘correct’ premium based on realized volatility and see if it was priced correctly. The next step is trading these past price differences