Target zone dynamics where the fundamental follows a SDE with periodic forcing

This paper investigates exchange rate and reserves dynamics in a target zone where the fundamental follows a stochastic differential equation with a periodic forcing function. Solutions to the model show that the target zone plays a stabilizing role but the dynamics of the exchange rate follow a family of S-shaped functions as time evolves. This dynamics cause the width of the target zone to be a varying function of time. It becomes what we can call a flexible target zone. The monetary authorities are then forced to hold not only large reserves but also varying reserves in order to properly defend the target zone.