This paper checks how international spillovers of shocks and policies are modified when banks are foreign owned. To this end we build a two-country macroeconomic model with banking sectors that are owned by residents of one (big and foreign) country. Consistently with empirical findings, in our model foreign ownership of banks amplifies spillovers from foreign shocks. It also strengthens the international transmission of monetary and macroprudential policies . We next use the model to replicate the financial crisis in the euro area and show how, by preventing bank capital outflow in 2009, the Polish regulatory authorities managed to reduce its contagion to Poland. We also find that under foreign bank ownership such policy is strongly preferred to a recapitalization of domestic banks. Finally, we check how foreign ownership of banks affects transmission of domestic shocks to find that it has a stabilizing effect.