DYNAMIC NUMERICAL-MODELS OF STOCK-MARKET PRICE - FROM MICROSCOPIC DETERMINISM TO MACROSCOPIC RANDOMNESS

A variant of threshold dynamics is introduced to model the behaviors o f a large assembly of dealers in a stock market. Although the microsco pic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations. The statistic al properties of market price change can be well approximated by a sim ple discrete Langevin-type equation with random amplification. The mac roscopic stochastic equation is solved both numerically and analytical ly showing that the market price change generally follow power-law dis tributions in the steady state. The reason for the appearance of rapid decay in the distribution tails are discussed. (C) 1998 Published by Elsevier Science B.V. All rights reserved.