yeah, but the closer to the realised median/median of that distribution over time, when estimating parameters, the better you would do right? or even better if you find the mispricings, then you would crush it on those wins. this assumes at least 1000's of transactions a year, but that's probably easily realistic at an IB.
I was going to bring up Garch to illustrate that you are a bit confused...
Garch may help you come up with a better estimate of Vol,which you could plug into BS,but once again,then what???
You plug in a higher IV,options appear cheap and you delta hedge?? Its not a directional bet,you do realise that.. You are trading Vol,not direction