This thesis consists of three essays on optimal monetary policy. In the first essay I study time-consistent monetary policy in an small open economy model with incomplete financial markets. I demonstrate the existence of two discretionary equilibria. The model is capable of explaining periods of different exchange rate volatilities as well as the transition between those regimes. Following a shock the economy can be stabilised either `quickly' or `slow', where both dynamic paths satisfy the conditions of optimality and time-consistency. I also show that a policy of partially targeting the exchange rate results in far worse welfare outcomes relative to a strict inflation targeting policy. In the second essay, I analyse how a policy maker can...