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