This paper investigates the statistical properties of high frequency nominal exchange rates and forward premiums in the context of a dynamic two-country general equilibrium model. Primary focus is on the persistence, variability, leptokurtosis and conditional heteroskedasticity of exchange rates and on the behavior of foreign exchange risk premiums. The model combines temporal dependencies in preferences with a transaction cost technology that generates a role for model. Agents in the economy make decisions on a weekly frequency and face shocks which display time-varying uncertainty. Simulation results reveal that the model accounts for the statistical properties of exchange rate data much more accurately than previous structural models.