Nonlocal onset of instability in an asset pricing model with heterogeneous agents

Empirical time series of financial market data, like day-to-day stock returns, exhibit the phenomenon that although usually tomorrow's price is unpredictable, the absolute value of the price change is correlated with the magnitude of past price changes; though the corresponding correlation coefficients are not very large, they are significantly different from zero. This phenomenon is known as `volatility clustering' in the financial liturature. In this note a micro-economic model of volatility clustering, introduced by Gaunersdorfer and Hommes, will be analysed. The deterministic skeleton of the model has a Chenciner bifurcation, and hence periodic points and invariant quasi-periodic circles coexisting with the `fundamental' equilibrium. Adding noise in form of stochastic supply shocks, volatility clustering is generated by the system jumping between the bases of attraction of the fundamental equilibrium (low volatility), and that of the non-fundamental attractor (high volatility).