Heterogeneity and feedback in an agent based market model.

We argue that two main ingredients in agent-based models (and in real speculative markets) which lead to realistic behavior of prices and trading volume are : heterogeneity (given the same source of information, market participants do not behave identically) and feedback (the individual demand of an investor for an asset is not only a function of the current price of the asset as in microeconomic equilibrium theory, but mainly depends on the recent history of the market prices). We then propose an agent-based model described in terms of few parameters which contains these two ingredients and show that the joint effect of feedback and heterogeneity leads to a market price which fluctuates endlessly and a volatility which displays a mean-reverting behavior : the volatility goes neither to zero nor to infinity in the long-run. The behavioral assumption is minimal : agents with threshold response towards information interact indirectly via the price. Heterogeneity is produced endogeneously because of the asynchronous updating process. Our agent-based model generically leads to absence of autocorrelation in returns, excess volatility, volatility clustering and endogeneous bursts of activity non attributable to external noise. Finally, the last part of the paper is a theoretical analysis focusing on the role of heterogeneity and its dynamics in this model