A few few notes:1) You posted an incomplete formula, d1 and d2 integrated under the standard normal CDF only represents how far in the money the underlying is expected to be and the probability of exercise respectively.2) I watched the first two videos and chunks of later ones, maybe I'll catch the rest when I have some time. However, the gist that I got from the videos is that they have the same misunderstanding of what Black-Scholes is actually used for as most academics do. Black-Scholes is not used as a pricing tool. We all know it's incorrect, there are far more profound concepts that we get from it than just a silly price. I'll leave it up to you to figure it out and/or post about it. 3) Skew correction is a good place to start in terms of quoting volatility. I've noticed your previous post on trading volatility, though looked them very throughly. If you're trading HV vs. IV (i.e gamma), using standard quoted IV is an issue and really a bespoke model w/ skew correction at the min should be implemented. Trading changes in just IV (i.e. vega) it's a bit iffy whether you need to go that complicated.
1) don't look to much into the image... it was just suppose to be an image relating to black scholes not the full calculation... i'll find a better image if I get time... 2) you're right! and thats part of our edge... most people just don't understand options, pricing tools, trading, etc3) the post on trading volatility is just a scan used to find names that could move and provide opportunity. But your comments are correct and appreciated.
ok image updated... if you find a better one shoot me the link! thx