This paper analyzes the interaction between crude-oil prices and the euro/US dollar exchange rate. Instead of focusing on long-run macroeconomic linkages like the bulk of the relevant literature, our approach takes on a financial-markets perspective using daily data. The fast-moving simultaneous impacts are identified through heteroskedasticity by specifying multivariate exponential general autoregressive conditional heteroskedastic processes for the structural variances. While no significance is found for the decade following 1986, subsequent oil-price changes cause inverse reactions in the dollar price and affect its volatility. Conversely, dollar appreciations asymmetrically induce increases in the oil price, at least up until the price drop in late 2008.