One of my commenters wrote in response to my piece Book Reviews: The Complete Guide To Option Pricing Formulas, and Derivatives, Models on Models:

1. Kurt Osis Says:
   December 13th, 20085:05 pm at EditDavid:

   How can advocate people using these models which clearly don?t work? Estimating volatility is a suckers bet. Even if you could estimate the underlying ?actual? volatility with 100% accuracy there would be sample error in your realized volatility. And of course the volatility isn?t just changing, the fundamentals of the underlying are changing.

   I once heard of a man named Mandelbrot who said volatility was infinite, in which case these sigmas and lemmas are a bit beside the point, no?

Kurt, I’ve met Mandelbrot, and have discussed these issues with him.? The two books that I recommended are also up on those issues.? Implied volatility estimates as applied to option pricing formulas are a fall-out.? No one thinks they are true, but they are a paramater used to keep relationships stable across options of similar expirations.

Intelligent hedgers hedge options with options; they don’t try to apply the theoretical equivalence that lies behind the traditional Black-Scholes formula and do dynamic hedging with the common stock itself.? That is the philosophy behind the books that I reviewed.

I’m on your page, Kurt.? Variance is infinite, and B-S blows up.? But within the options world, there has to be a way of calculating relative value, and these books aid us in that calculation.

If you think I am wrong here, go to your local library, and get these books via Interlibrary loan.? Read them, and you will see that we are all in agreement.