Target Zones and Interest Rate Variability
The trade-off between interest rate variability and the width of an exchange rate target zone is examined, using the regulated Brownian motion model of target zones. It is shown that for narrow exchange rate bands, and for reasonable parameter values, the interest rate differential's asymptotic variability is increasing in the width of the exchange rate band; whereas for wide exchange rate bands it is slowly decreasing in the exchange rate band. The interest rate differential's instantaneous variability is decreasing in the width of the exchange rate band.
A narrow target zone differs from a completely fixed exchange rate regime in that the interest rate differential's instantaneous standard deviation is high and even increases when the zone narrows.
The model is extended to include a realignment/devaluation risk, as well as an endogenous exchange rate risk premium. The risk premium is small for reasonable parameter values and does not matter much.