Symmetry breaking in a bull and bear financial market model

Abstract

We investigate bifurcation structures in the parameter space of a one-dimensional piecewise linear map with two discontinuity points. This map describes endogenous bull and bear market dynamics arising from a simple asset-pricing model. An important feature of our model is that some speculators only enter the market if the price is sufficiently distant to its fundamental value. Our analysis starts with the investigation of a particular case in which the map is symmetric with respect to the origin, associated with equal market entry thresholds in the bull and bear market. We then generalize our analysis by exploring how novel bifurcation structures may emerge when the map’s symmetry is broken.