Abstract: In recent years, the strong fluctuations in crude oil prices bring many uncertain factors to the stable development of real economy, so there is an important theoretical and practical significance in accurately characterizing and predicting the extreme volatility riskamong various crude oil markets. In this paper, combining extreme value theory(EVT) with fivecategories of R-vine copula models, the extreme dependence relationship between six crude oil markets is depicted. Based on that the value at risk(VaR) and expected shortfall(ES) models are constructed to measure the out-of-sample extreme risk using a sliding time window method. Finally, a backtesting for unconditional coverage and backtesting based on bootstrap are, and carried out the VaR and ES measurement accuracy of different models is compared. The empirical results are summarized as follows:(1) Mixed R-vine-EVT model can describe the extreme dependence relationshipamong various crude oil marketsmore excellent and show a better risk measures efficiency.(2) VaR model can well depict the riskstatusat low risk levels, while the measure precision at high risk levels is insufficient. On the contrary, ES model shows a better risk measurement capability at the high risk levels.Accordingly, some practical suggestions are put forward e.g., investors should introduceextreme value theory to describe the extreme risk situation of crude oil markets; under the background of sharp fluctuations in international crude oil prices, Mixed R-vine model can more adapt to the changes of dependency relationship among various crude oil markets.

Key words: crude oil market, R-vine copula, extreme value theory, value at risk, expected shortfall, backtesting