Long Swings in Exchange Rates: a Stochastic Control Approach

A regime-switching model to describe the exchange rate dynamics is derived as solution to a stochastic control problem. We assume exchange rates evolve according to some macroeconomic variables whose dynamics could be described by a Brownian motion with a state-dependent drift. The local Monetary Authority is assumed to intervene influencing the evolution of the fundamental, causing the exchange rate to switch from a depreciating to an appreciating regime (and vice versa). We assume the behaviour of the Monetary Authority can be modeled using an optimal control framework where the state variable is represented by the fundamental. The solution of the model allows the determination of an endogenous tolerance band within which the exchange rate freely fluctuates.