Volatility clustering in agent based market models

We define and study a market model, where agents have different strategies among which they can choose, according to their relative profitability, with the possibility of not participating to the market. The price is updated according to the excess demand, and the wealth of the agents is properly accounted for. Only two parameters play a significant role: one describes the impact of trading on the price, and the other describes the propensity of agents to be trend following or contrarian. We observe three different regimes, depending on the value of these two parameters: an oscillating phase with bubbles and crashes, an intermittent phase and a stable ‘rational’ market phase. The statistics of price changes in the intermittent phase resembles that of real price changes, with small linear correlations, fat tails and long-range volatility clustering. We discuss how the time dependence of these two parameters spontaneously drives the system in the intermittent region.