L. Gardini, University of Urbino Carlo Bo, Urbino, Italy
D. Radi, Catholic University of Sacred Heart, Milan, Italy
N. Schmitt, University of Bamberg, Bamberg, Germany
I. Sushko, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
F. Westerhoff, University of Bamberg, Bamberg, Germany

Abstract: We develop a foreign exchange market model in which a market maker adjusts the exchange rate with respect to the trading behavior of chartists, fundamentalists and a central bank. While chartists bet on the persistence of bull and bear markets, fundamentalists speculate on mean reversion. The central bank seeks to stabilize the foreign exchange market by placing buy (sell) orders when the undervaluation (overvaluation) of the exchange rate exceeds a certain threshold. Since a one-dimensional piecewise-linear discontinuous map with three branches determines the evolution of the exchange rate, we use a combination of analytical and numerical tools to explore the extent to which the central bank is able to tame the behavior of the foreign exchange market.

Keywords: exchange rate dynamics, chartists and fundamentalists, central bank interventions, piecewise-linear discontinuous maps, stability, bifurcation