This paper analyzes optimal monetary policy in a two-country model with asymmetric shocks. Agents insure against risk through the exchange of Arrow- Debreu securities. Although central banks commit to the policy that maximizes domestic welfare, this does not lead to price stability. In an attempt to improve their country’s terms of trade of securities, central banks may choose an inflationary policy rule in good states. If both central banks do so, the effects on the terms of trade wash out, leaving both countries worse off. Countries facing asymmetric shocks may therefore gain from monetary cooperation