Heterogeneous speculators, endogenous fluctuations and interacting markets: a model of stock prices and exchange rates

We develop a discrete-time model in which the stock markets of two countries are linked via and with the foreign exchange market. The foreign exchange market is characterized by nonlinear interactions between technical and fundamental traders. Such interactions may generate complex dynamics and recurrent switching between “bull” and “bear” market phases via a well-known pitchfork and period-doubling bifurcation path, when technical traders become more aggressive. The two stock markets are populated by fundamentalists, and prices tend to evolve towards stable steady states, driven by linear laws of motion. A connection between such markets is established by allowing investors to trade abroad, and the resulting three-dimensional dynamical system is analyzed. One goal of our paper is to explore potential spill-over effects between foreign exchange and stock markets. A second, related goal is to study how the bifurcation sequence which characterizes the market with heterogeneous speculators is modified in the presence of interactions with other markets.