Optimal Exchange Rates: A Stochastic Control Approach

Abstract

We present novel formulas for the determination of the optimal values of the exchange rate and the external (foreign currency) debt. A stochastic differential equation is developed that relates the net worth of an economy to both its exchange rate and level of external debt. Using the martingale optimality principle, the optimal values for the exchange rate and the external debt are derived. Applied to Egypt, we find that its actual nominal exchange rate has stayed above its optimal value since the early 1990s, except for two years, and that the actual external debt-to-net worth ratio is lower than the optimal one for most of the time. Since 2013 the actual external debt-to-net worth ratio is close to the risky levels of the optimal values.