We analyze optimal monetary policy in a small open economy characterized by home bias in consumption. Peculiar to our framework is the application of a Ramsey-type analysis to a model of the recent open-economy New Keynesian literature. We show that home bias in consumption is a sufficient condition for inducing the monetary policymaker of an open economy to deviate from a strategy of strict markup stabilization and contemplate some (optimal) degree of exchange rate stabilization. We focus on the optimal setting of policy both in the case of firms setting prices one period in advance and in a gradual fashion subject to adjustment costs. While the first setup allows us to analytically highlight home bias as an independent source of equilibrium markup variability, the second setup allows to study the effects of future expectations on the optimal policy problem and the effect of home bias on optimal inflation volatility. The latter, in particular, is shown to be related to the degree of trade openness in a U-shaped fashion, whereas exchange rate volatility is monotonically decreasing in openness.