Abstract
We examine an asset pricing model of Westerhoff (2005). The model incorporates heterogeneous beliefs among traders, specifically fundamentalists and trend-chasing chartists. The form of the model is shown here to be a nonlinear planar map. Since it contains a single parameter, the model may be considered the simplest effective model yet derived for financial asset pricing with heterogeneous trading. Analysis of the map yields results for stability and bifurcations of fixed points and periodic orbits. The model has intricate attractor basin behavior and global bifurcations to chaos: symmetric homoclinic bifurcation and boundary crisis.
Highlights
The notion that the interaction of investor classes can be expressed as discrete dynamical systems is not new
Because the models are naturally formulated to consider the interactions of various identifiable trading groups and because the observable variables such as asset price and trading volume are essentially discrete, the models fall into the branch of mathematics known as discrete dynamical systems, maps, or difference equation systems
Heterogeneous trader models are a viable alternative to the usual stochastic calculus-based models of market behavior
Summary
The notion that the interaction of investor classes can be expressed as discrete dynamical systems is not new. Because the models are naturally formulated to consider the interactions of various identifiable trading groups and because the observable variables such as asset price and trading volume are essentially discrete, the models fall into the branch of mathematics known as discrete dynamical systems, maps, or difference equation systems. This contrasts with 17 , where purely numerical simulations are performed. Its thorough analysis in this paper will help to guide the formulation and analysis of more detailed models of markets with interacting heterogeneous agents
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