David,
I guess you have to replace the diffusion equation (which is known to describe Gaussian market, also known as Black-Scholes) with fractal diffusion. I don't know yet about Mandelbrot - I have to see the book. It will be delivered in about 7 days :) I know the book you were talking about. I looked through it in a library, and it got me interested in looking into fractals. I guess, it should have fractal diffusion equation in it, if I remember correctly. But fractional differentiation per ce does not tell you much.
I'm a theoretical physicist by education, although, unfortunately, I never did chaos as a part of my profession.
I'm determined to learn about it, though. The Hurst exponent does not tell you much about the markets, too - as much as, say, the Gaussian distribution. The fractal dynamics is buried in the "fat tails" which have power law dependence (Levy). There are pretty detailed articles about the behavior of the markets in the physics journals (Mostly Physical Review E), as this remains a heavily researched field. You should not fool yourself that you discovered something "new". All these brokerage firms and hedge funds have theoretical physics Ph.Ds (quants) working for them. That particular book (Bouchard and Potters) is a reasonably up to date book on what is known about the fractal nature of the markets right now, including the period 1995-2000, when there was a heavy hiring of theoretical physicists in finance to develop the field (they quickly discovered it pays off LOL!). Heavy things like "Random matrix theory" used to describe chaos. I still need to learn all this stuff. Then again - you have correlations between different markets, which you also need to measure and use. So you need to look at a more complete picture than just 1 market index (say, SP500).
Computers right now have more than enough power to do all this stuff after the market close. So it will pay to learn about it. Certainly, these books are a better investment than the brokerage fee or spread that you pay to buy or sell several option contracts... Especially given the statistics that you lose, most of the time. LOL!
I have the book by Richard M. Crownover - Introduction to Fractals and Chaos, to learn the basics. |
