Probability Analysis of Exchange Rate Target Zones

The objective of this paper is to show quantitative results for the exchange rate target zones in a small open economy. We develop a stochastic model for exchange rates under the equilibrium in goods and money markets based on a variation of Dornbusch (1976)'s model, incorporating several kinds of macroeconomic shocks and a noneconomic factor ignored by literature. Using the theory of stochastic differential equation (SDE) in probability theory, we calculate the probabilities that the nominal exchange rates reach the boundaries of the target zones for the first time, and the mean time that the nominal exchange rates remain in the target zones. Furthermore, using our explicit expressions of the fundamental factor and the defnite relationships between the variables, we analyze the effects on the probabilities from macroeconomic and non-economic factors, such as the elasticity of the premium rate of exchange rates, the fundamental factor, and the volatilities of the shocks.