Speculative behaviour and complex asset price dynamics: a global analysis

This paper analyses the dynamics of a model of a share market consisting of two groups of traders: fundamentalists, who base their trading decisions on the expectation of a return to the fundamental value of the asset, and chartists, who base their trading decisions on an analysis of past price trends. The model is reduced to a two-dimensional map whose global dynamic behaviour is analysed in detail. The dynamics are affected by parameters measuring the strength of fundamentalist demand and the speed with which chartists adjust their estimate of the trend to past price changes. The parameter space is characterized according to the local stability/instability of the equilibrium point as well as the non-invertibility of the map. The method of critical curves of non-invertible maps is used to understand and describe the range of global bifurcations that can occur. It is also shown how the knowledge of deterministic dynamics uncovered here can aid in understanding the behaviour of stochastic versions of the model.

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