The degree of international risk sharing matters for how monetary policy should optimally be conducted in an open economy. This is because risk sharing affects the way in which monetary policy is affected by terms of trade considerations. In a standard two-country model with monopolistic competition and nominal rigidities I consider different assumptions on international financial markets - complete markets, financial autarky and a bond economy - and a large region for the crucial parameter of the trade elasticity. There are three main results: one, the prescription of (producer) price stability as the optimal policy is obtained only as a special case, while in general it is optimal to deviate from a strictly zero inflation rate. Two, while gains from international policy coordination are generally small, they become potentially substantial when international risk sharing is poor and wealth effects from shocks across countries are large. And, three, when international financial markets are incomplete, there are also (sometimes considerable) gains over the flexible price allocation achievable.