A Target Zone Model Where the Fundamentals Follow a Geometric Brownian Motion

Abstract

In this paper, we propose a model of exchange rate target zone based on a specification of the economic fundamentals known as a Geometric Brownian Motion. The rationale behind this specification is that the fundamentals series is not necessarily normally distributed as commonly assumed, as indicated by its excess kurtosis and ARCH properties. Therefore, assuming a normal specification can be problematic. The main difficulty is that with such a specification finding a closed form solution for the model becomes somehow more involved. We present some results in which the exchange rate formula is explicitly derived. Then we look at several types of central bank interventions in the foreign exchange market such as Krugman’s marginal interventions, central bank interventions a la Caballero and central bank interventions a la Flood-Garber. In addition, we present some empirical investigations where it is found that, for the most part, these exchange rate models do not fit the data well and a case where the model performs satisfactorily. We believe that the sources of the problem may reside in the complexity of estimating the models efficiently given that the theoretical approach is quite sound.