We present a simple financial market model with interacting chartists and fundamentalists. Since some of these speculators only become active when a certain misalignment level has been crossed, the dynamics are driven by a discontinuous piecewise linear map. The model endogenously generates bubbles and crashes and excess volatility for a broad range of parameter values - and thus explains some key phenomena of financial markets. Moreover, we provide a complete analytical study of the model's dynamical system. One of its surprising features is that model simulations may appear to be chaotic, although only regular dynamics can emerge.financial market crisis; bull and bear market dynamics; discontinuous piecewise linear maps; border-collision bifurcations; period adding scheme.