This Paper analyses the implications of financial market structure for the existence and size of welfare gains from international monetary policy coordination. Policy coordination is analysed in a two-country stochastic general equilibrium model simple enough to yield explicit analytical solutions. Welfare gains from coordination are found to be largest when: the elasticity of substitution between home and foreign goods differs from unity; international markets in state-contingent assets allow full consumption risk sharing; and asset trade takes place before monetary policy rules are determined. Welfare gains are found to be much smaller when there are no international financial markets.