We develop a three-dimensional nonlinear model in which the stock markets of two countries are linked via and with the foreign exchange market. The foreign enchange market is modeled in the sense of Day and Huang (1990), i.e. we consider nonlinear interactions between technical and fundamental traders. Accordingly, the fractions of technical and fundamental traders is fixed, but fundamental traders rely on a nonlinear trading rule. The two stock markets are expressed in a linear way. In such an environment the markets are interdependent. First, stock markets traders who invest abroad have to consider potential exchange rate adjustment. Second, there agents obviously need foreign currency to conduct their trades. As it turns out, our model consist of three coupled difference equations of which the one describing the foreign exchange market is nonlinear. We can, however, reduce the dimension of the model assuming, for instance, that fundamental traders from a country A are excluded from trading in the other country H. If we also assume that fundamental stock traders from H do not paertecipate in stock market A, then both stock markets are decupled from the foreign exchange market. Our goal is to explore how the coupling of financial markets may affect the emergence of bull and bear markets. We find that when a critical parameter is varied the unique stable fundamental steady states becomes unstable and two new stable non-fundamental steady states emerge, one above (bull) and one below (bear) the fundamental. Then, the new steady states undergo a 'cascade' of flip-bifurcations, leading to chaos. At some point, the two chaotic areas merge forming a unique chaotic attractor characterized by intricate price fluctuations and switching between bull and bear markets, at unpredictable points in time.

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