We give a stochastic microscopic modelling of stock markets driven bycontinuous double auction. If we take into account the mimetic behavior oftraders, when they place limit order, our virtual markets shows the power-lawtail of the distribution of returns with the exponent outside the Levy stableregion, the short memory of returns and the long memory of volatilities. TheHurst exponent of our model is asymptotically 1/2. An explanation is also givenfor the profile of the autocorrelation function, which is responsible for thevalue of the Hurst exponent.
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