It takes care of the pricing problem as far as the market currently prices it. Whether or not this is realistic is another story. The problem of using potentially more realistic pricing models is that if the "market" uses another model, you'll face mark-to-market problems, right ? I'm not saying you'll not ultimately make money though, you might very well. From my experience having a middle office reeval you product using another model than the one widely accepted by the market is challenging. No matter how good your model is.
I'm doing credit derivatives and we're having the same doubts right now about our models. Copula based algorithms based on JP Morgan theories but which nobody really understand why we use them, and even less people will know how to build these models. The choice of the particular Copula to use is even more a mystery and completely arbitrary as there is no rationale to use one or another. There's been a few research papers proposing alternative pricing methodologies but it could be a long while before people dare using them, as they provide significantly different prices. That's the very big difference between theoretical research and the reality of the markets, or the difference between a University prof (no disrespect intended) and somebody actually trading the product.
==================== Last point was a good one; even if memory serves me correctly one of Black Scholes, was a prof , apparently a rather orderly prof. Wouldnt necessarly discard a warped , well used yardstick; especially if one has some accurate steel tapes. In other words even when they get the profit & most of math right; may not rubber stamp the assumption that , the probablilties are the same for checking price price daily or weekly.
Thanks for everones input. Perhaps I should put the question to you as this. Based upon the "fat tails" problem or the fact that normally distributed returns tend to be abnormally volatile: How do you model options? I was under the impression the big investment banks use something other than black scholes - what do you use?
Why would you say that? The real trick to getting the skew problem right is getting the hedges to be 'skew compliant'. A vol model would have to fit the current skew and replicate the dynamics of the skew as both the ATM vols and forwards move around. There is a class of vol models that do that very well and you can over or under hedge the deltas and vegas on puts/calls to achieve a consistent set of deltas and vegas across the strike space.
You could (I believe successfully) use the following: - BS for pricing of European style options; you will need to model the volatility smile - Binomial for pricing of American options - BS for the 'Greeks' The IB TWS has the section Option Analytics. Both models are available in it.
Hey sle, hope all is well- Modeling the skew in an attempt to flatten the strip-vols to the benefit of the model being implemented. I'd be interested in any new maths that allowed for skew-arbitrage to be realized.