How do the financial markets behave?

Benoit Mandelbrot, one of the world's most celebrated mathematicians, believes that our understanding of the stock market is as misleading as medieval astronomy. But he thinks that he now has the tools to fundamentally revise economists envision.
Well..... the change could be as radical as moving the Earth from the center of the solar system to an orbit round the sun !!! .......That's Cool! :)

More than 40 years ago, Mandelbrot discovered a new kind of math: Instead of accounting for neat and tidy geometry, his new equations described shapes with general patterns repeating in new and unexpected ways. He named these new mathematical equations fractals, and in the intervening decades they have been used to describe coastlines, clouds and air turbulence, to create computer graphics and to model the way rocks and sheets of metal wear, fragment and crack. (I sometimes think why we, people other than scientists, can not notice or simply ignore the self evident natural harmony in universe.. peh awareness....)

Anyway, Mandelbrot has brought the fractal toolbox back to the field of price variation, where he made vital contributions decades ago.

I read a book of him few months ago, namely "The (Mis)behaviour of Markets" . I should go over it throughly once more. It chronicles Mandelbrot's forty-year quest to understand how the stock market works, and his search for a better mathematical model. Using the techniques of fractal geometry, which he himself invented, Mandelbrot believes he has finally realised his ambition. ( there are certainly few ppl around who hit their ambitions in life... i know...key is dedication...) But getting his ideas to be taken seriously has proven even more difficult.

Mathematicians make models based on patterns, and the problem with the stock market is that there aren't any patterns. In fact, trying to predict how much a share price will rise or fall may seem like trying to predict the weather — though that hasn't stopped people from trying.

The wild behaviour of financial markets, which makes them so risky. Are mathematicians inspired from history..? The tale of Harold Edwin Hurst, for example, who analysed the flooding of the Nile, is one of the gems that are dotted throughout the book.

The book is actually not for dummies but is clearly written with non-mathematicians in mind. Unlike some mathematicians, Mandelbrot doesn't depend on algebra and equations to make his point. (Thanks to him!!)

Mandelbrot refers to the turbulence he finds in nature and financial market behavior as "roughness." The more turbulent the distribution, the larger his quantitative measure of roughness. The mathematics of roughness is Mandelbrot's contribution to the science of measuring the non-normality in otherwise stable distributions, which he calls "fractal geometry." By mathematically defining roughness, Mandelbrot can, with economy of inputs, among other things, produce charts on market behavior that mimic the real thing. By tweaking the inputs, one can introduce greater or lesser degrees of roughness into the charts of market returns. According to Mandelbrot, different markets are characterized by varying degrees of roughness. The rougher the market, the greater the underestimation of risk made by the modern finance tool kit. Adding more complexity to the fractal model (multi-fractal models) produces additional sophistication to mimicking more complex market behavior, clustering, and time interval effects.

What I know cannot be used to pick stocks, trade derivatives, or value stock options; time, and further research by others, will determine whether it ever can." Mandelbrot does find value in fractal geometry for imitating financial market reality, offering "some insights into how markets work."