Thursday 2010-09-16

Fractals and Scaling in Finance by Benoit Mandelbrot

This is a collection of papers mapping out Mandelbrot's major points in finance.

"Price discontinuity and centtration are major ingredients in a realistic evaluation of risks.... In paticular, price continuity is an essential (bu seldom mentioned) incredient for all trading schemes that prescribe at what point one should buy on a rising price and sell on a sinking price. Being discontinuous, actual market prices will often jump over any prescribed level, therefore, such schemes cannot be implemented."
-- Discontinuity and Scaling, 1.4
The absence of structure predicted by Markov clearly contradicts well-founded legend and historical facts. The Bible describes "seven fat and seven lean years" and history records periods of seventy wet and fat years of famous Pharaohs followed by seventy dry years ruled by forgotten dynasties.
-- Discontinuity and Scaling, 4.3

(1) Large price changes are much more frequent than predicted by the Gaussian; this reflects the "excessively peaked" ("leptokurtic") character of price relatives, which has been well-established since at least 1915.

(2) Large practically instantaneous price changes occur often, contrary to prediction, and it seems that they must be explained by causal, rather than stochastic models.

(3) Successive price changes do not "look" independent, but rather exhibit a large number of recognizable patterns, which are, of course, the basis of the technical analysis of stocks.

(4) Price records do not look stationary, and statistical expressions such as the sample variance take very different values at different times; this nonstationarity seems to put a precise statistical model of price change out of the question.

-- The Variation of Certain Speculative Prices