Dynamical systems models of asset pricing

Kirby, Natasha (2006) Dynamical systems models of asset pricing. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this thesis we study asset pricing models using a dynamical systems approach. We first review the literature on current dynamical systems models of asset pricing. The foundation of these models is the fact that they incorporate heterogeneous beliefs among traders. Two main trader groups are discussed, fundamental traders and trend-chasing chartists. The theory of discrete dynamical systems, or maps, is also explored, and in depth analysis of these models is carried out. We modify a model of Chiarella, Dieci and Gardini to incorporate a third group of traders called contrarian chartists. The main idea surrounding contrarian chartists is that they not only disagree with the majority of traders, but they choose when to act on the disagreement in order to make a profit. A second case of this model is also discussed, where contrarian chartists are thought to always disagree with the majority. This case reduces to the literature model with one different parameter value. In each case, the model consists of a system of two difference equations. The first equation represents the logarithm of the asset price at any given time t, and the other represents the expectation of price change from one time period to the next. This system exhibits complicated behaviour including local behaviour such as period-doubling and Neimark-Sacker bifurcations as well as local attractors, global bifurcations and chaos. The results in terms of asset prices are also included for these models. The thesis concludes with some limitations and suggestions for future research.

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