The Complete Guide To Option Pricing Formulas, and Derivatives, Models on Models (II)

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:
    David:

    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.