Heterogeneity and feedback in an agent-based market model.
Résumé
We propose an agent-based model of a single-asset financial market, described in terms of a small number of parameters, which generates price returns with statistical properties similar to the stylized facts observed in financial time series. We 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. Our agent-based model generically leads to absence of autocorrelation in returns, stochastic volatility, excess volatility, volatility clustering and endogeneous bursts of market activity non-attributable to external noise. The parsimonious structure of the model allows to identify the mechanism leading to these effects. We investigate theoretically some properties of this model and present numerical simulation of other properties.