True, but isn't the point of doing something is ... to do it well? Well as in get better and better, not just good enough.
It is a generally accepted practice, even in engineering. You take a very complex system, develop first order approximation, usually a close form solution, then if more accuracy is needed, you add second order terms... BS is exactly the same, a first order close form solution.
ok. So while @ironchef definitely summed my point way better than I did. I now totally get what @taowave and @poopy are saying (even if poopy is a grumpy anger ball). And indeed I was ignorant of the use case because of my inexperience in your position. I still do believe there could be a better method that is pretty low hanging fruit, however, I now understand why good enough and mathematically tractable is preferable to lower bias in the face of data, because for the most part in your use case, you are creating the data or there just isn't data available and everybody in that transaction is all good with that. And, thanks to mr. Kevin's really interesting post, maybe what's important about the model is not the absolute price and it's weakness due to the IV flaw we've discussed, but what BS does do well is estimate greeks, in other words relative price. At the end of the day, you already have a market to price the asset, and what we really might need a model for is the greeks. Anyways, thanks for humoring my aggressive half-truth Socratic questioning. I think I really get something I was not expecting to get. Am I getting closer here? Shall we have a warm Hegelian moment? Or am I still missing stuff on the whole?
So do you find that garch or just some running estimate fixes the the flaws? Shouldn't it then actually find any mispricing pretty well, should it exist?
All is good... There could be a "better" method/model,and as I mentioned.if you are trading the listed markets,with tight bid ask spreads,how is it going to help??? If your model estimates a vastly different value/greeks than Black Scholes,are you planning on delta hedging at your "hedge" vol to realise your forcasted theoretical edge?? Will you hedge at a vastly different Delta than what BS spits out??? I dont think so
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