Fractals And Scaling In Finance Book

Benoit Mandelbrot is the inventor of the mathematical concept of fractals. His earlier book The Fractal Geometry of Nature was a truly groundbreaking book about fractals and how they are seen in nature. In The Misbehavior of Markets he turns his attention to the application of fractal concepts to markets. Mandelbrot shows that price fluctuations:
1) are not independent from one time period to the next
2) appear to be the same, regardless of the time scale involved (hours/days/months/years)
3) do not obey a Gaussian (normal bell-like) distribution, but instead follow a power-law distribution.
These characteristics are exactly the opposite of the assumptions that are normally used in financial circles. As a result, most financial models severely under-estimate financial risk. Most financial models use certain parameters (like the beta factor) that purport to measure price volatility. Mandelbrot shows that many of these parameters are worse than useless; they are so wrong, they are dangerous and can lead to world-wide financial ruin.

This book is also somewhat of a biography; Mandelbrot details some of the fascinating aspects of his life, and that of his parents. One of the reasons contributing to his move from France to the U.S. is the disdain of French mathematicians to applied research. The only problem with this book is that Mandelbrot writes in a tone that is too strident for my taste. Nevertheless, I strongly recommend this book to anyone with an interest in applied mathematics or finance.