A Bloomberg article today about black-Scholes and the recent arguments against it.. http://quote.bloomberg.com/apps/news?pid=10000039&refer=columnist_crystal&sid=aokOnbAVHoYw
I've seen many different models, and they all have some weakness. Maybe one give you a more accurate gauge of skew with prices where there are now, but on a decent move everything gets out of whack. Or maybe it behaves better on bigger moves, but you have difficulty setting the skew right here. The important thing is to know what the weaknesses are of our model, and make the adjustments necessary, cuz there ain't no holy grail of option models. If there is (by some strange chance) none of us here can afford it. FWIW, back when I was on the floor, I knew of several groups paying up to $500,000 for the better proprietary models (which still aren't perfect, but react to market moves better than standard models). And as crazy as it sounds, the $500,000 was easily recouped. Vega
Back when I was clerking for a market makker LLC, the clearing firm offered a "modified" binomial tree model ( Cox- Rubenstein) as an alternative to Black Scholes. I believe it did two sets of tree calculations at different steps that were averaged out for "smoother" values. Alot of the MM's liked it.
30 years ago, it was state of the art. It's the basis for a lot of better and more current models, but it was based on some flawed assumptions, e.g. normal distribution of prices, rather than kurtotic. Used in its original form, it will entice you to sell cheap OTM options and underestimate their value, which has bankrupted a lot of traders. Everyone now adjusts their models in some proprietary way to adjust for the weaknesses. Jessie
In the book "The Business of Options" Martin O'Connell tells about an options seminar he spoke at and one of the speakers was Myron Scholes. Dr. Scholes was giving his presentation and during it one of the participants kept hassling him, finally saying "Your model is just plain wrong." Dr. Scoles dryly answered "Of course, it's wrong. That's why we call it a model."
Interesting points.. Also I think the recent debates regarding Black-Scholes formula maybe mostly related to the fact that now some companies need to expense the stock options. So they may use the Black-Scholes formula to come up with expense figures for those options...
The problem of Black Scholes model with Employees' stock option mentioned in that article is quite different from what we have when used in trading, although both have a lot to do with the use of volatility. Because of the long term nature of employee stock options, it's almost impossible to get a good estimate on the stocks' volatility and therefore their option values. In trading, using volatility smile (a direct violation to one of the BS assumptions) "solves" BS model's pricing problem but leaves problem with the Greeks, making your portfolio hedging a big headache with regard to underlying movement, i.e. the delta and gamma. BS's Vega and theta seem OK. There are stochastic volatility models out there to overcome this problem.
"it has outlived its usefullness" Nothing will ever replace BS for calculation of implied vols of the market. Similariliy, if you have a good local vol model (i.e Derman/Kani or Heston or any other) for interpolating vols between liquid points, BS is the best way to get the price. For tree-based pricing, do not forget that BS is still used to calibrate the trees.