At this point it's pretty much just a quoting convention... I don't think any is trading with it anymore (dynamic hedging with BS delta is pretty much suicide).
Support and resistance is not factored into the model. IMO, you make money when you sell options below strong support, etc.
Basically all of the assumptions of the original model are flawed plus it only works for European style options (and almost all the options in equities are American). - Ability to short the underlying -> flawed, in some instances even when you can short you will be charged outrageous interest on it (for hard to borrow securities). - One single interest rate (risk free) -> flawed, rates for borrowing and lending are different plus each trader has different credit profiles and presumably can borrow money at different rates. - Constant volatility for the underlying -> no need to even say it is flawed. - Continuous hedging -> Impossible, impractical. There is no way you can hedge an infinite amount of times per day (transaction costs etc.). -Log returns being normally distributed -> flawed, rarely we see a Gaussian distribution of returns out in the wild. As you can imagine in real life no one prices options with BSM, however because professional option traders quote options prices in IV (implied volatility) units, the BSM is used as an standard way to obtain the quoted IV from price.
My comments. Don't know how helpful since I do not have any formal finance training. I find that using it as a quick and dirty approximation to assess a strategy is not too bad. It tends to give good general viability of the strategy. Can't comment since I never short any underlying. I find this to be not too much of a problem as I can program in my own carrying rate or a variable interest rate if I know what direction the rate is going to be. Yes, I find this the biggest problem for my analysis but how do I deal with this? Appreciate any guidance. Since I don't hedge would this be a problem for me other than the starting assumption is not accurate? Can you comment on how one models fat-tails instead of lognormal? The advantage with BSM, for me, is actually I can deal with all the inaccuracy with one parameter: IV. But it also means that my assessments will have a big error if I rely on BSM. What is the best way out other than buying a high price complex algorithm?
Ironchef, is just that the assumptions that give rise to the model are flawed. Therefore whatever answer that the model provides is flawed too. However, that doesn't mean that the model is useless. In this case BSM provides us with a closed form solution (read nice equations) for the problem so we can study the nature of the problem and also so we can improve upon them. It does provide insights into the pricing problem. The people most obsessed with correct prices are of course dealers and big vol players. But even for retail players there is hope. Even the lowly binomial model can price options with any kind of arbitrary conditions (variable vol, fat tails, transaction costs, etc).
I only program/compute in Excel. Can I find a binomial equation using Excel? If so, how do I program in fat tails? Thanks and I appreciate your coaching.
Hoadley has been doing Excel option tools for a long time. You might take a look: http://www.hoadley.net/options/strategymodel.htm