In this paper we develop a two-country global monetary economy where a monetary equilibrium exists because of fundamentaldecentralized trade frictions ? a Lagos-Wright search and matching friction. In the decentralized markets (DM), the terms of trade can be determined either by bargaining or by competitive price taking (baseline model). We show that the baseline model is capable of generating quite realistic real and nominal exchange rate volatility observed in the data, without relying on more ad-hoc sticky price assumptions commonly used in the international macroeconomics literature. The key mechanism lies in the role of search and matching frictions and a primitive technological assumption ? that capital is also a complementary input to production in the DM. This creates an internal propagation mechanism by modifying asset-pricing relations and relative price dynamics in the model.