This study constructs a flexible range-based volatility model by considering extreme-value information to explore the volatility and dependence structures between the oil price and the US dollar exchange rate. An asset-allocation strategy is implemented to evaluate the economic value and confirm the efficiency of this model. The empirical results indicate that the use of extreme-value information can not only enhance the explanatory power of volatility structures, but also sort out the asymmetric volatility effect in the oil market. Besides, investors can obtain extra benefits of between 72 and 713 annualized basis points by incorporating extreme-value information into their asset-allocation strategies; less risk-averse investors can generate higher benefits. The empirical results have potentially important implications for asset allocation and risk management.