This paper investigates the problem of the risk management for an import firm by using crude oil options. We propose a new risk measure (thereafter called CVaRMD) that synthesizes the mean and median deviation of the hedged portfolio loss to trace the extreme risk. The classical volatility models (GARCH-n, GARCH-t, GJR-n and GJR-t) are commonly-used in finance literature to depict the marginal distributions of the oil price and the exchange rate. Different from the time-consuming method of simulation, we employ Copula functions to deduce the cumulative distribution function of the hedged portfolio and then to calculate the extreme risk. Empirical studies demonstrate that GARCH-n and GARCH-t models are better to forecast the volatilities of Brent crude oil price and the exchange rate (CNY/USD)respectively. Frank copula better portrays the correlation structure between Brent crude oil price and the exchange rate. We find that hedging with crude oil options can reduce the extreme risk effectively. By comparing the skewness of the extreme loss under two risk measures of Conditional value-at-risk (CVaR) and CVaRMD, we find that the left deviation degree of the extreme loss under CVaRMD criterion is greater. The result of variance analysis further confirms this conclusion. That is to say, based on the strategy of minimizing CVaRMD, the extreme loss risk that the firm faces is relatively smaller. We further analyze the parameter sensitivities and give the firm some suggestions to choose the appropriate option contracts and decide its budget. © 2018, Bucharest University of Economic Studies. All rights reserved.