Percolation Models of Financial Market Dynamics

Microscopic models dealing with the decisions of traders on the market have tried to reproduce real market behaviour. Possibly the simplest of these models is the herding approach of Cont and Bouchaud. Variations include letting the concentration varying between zero and unity (or zero and percolation threshold); changing the price proportionally not to the difference between demand and supply, but to the square root of this difference; influencing the buy/sell decisions by the actual price and price change. As a result, the probability to find a market change greater than some R was found to vary as R-2.9; this distribution gets wings which might correspond to outliers like the 1929 crash on Wall Street; bubbles lead to sharp peaks separated by flat valleys; and the log-periodic variations after the Japanese crash of 1990 were reproduced to get rich from the prediction made in January 1999 by Johansen and Sornette that Nikkei will rise appreciably during 1999. As it did.

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