Stochastic multiplicative processes for ÿnancial markets

Abstract We study a stochastic multiplicative system composed of ÿnite asynchronous elements to describe the wealth evolution in ÿnancial markets. We ÿnd that the wealth uctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated LÃ evy-like distribution, and the cross-correlation between relative updated wealths is the origin of the nontrivial properties of returns, including the power-law distribution with exponent outside the stable LÃ evy regime and the long-range persistence of volatility correlations. c 2002 Published by Elsevier Science B.V