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The use of parametric GARCH models to characterise crude oil price volatility is widely observed in the empirical literature. In this paper, we consider an alternative approach involving nonparametric method to model and forecast oil price return volatility. Focusing on two crude oil markets, Brent and West Texas Intermediate (WTI), we show that the out-of-sample volatility forecast of the nonparametric GARCH model yields superior performance relative to an extensive class of parametric GARCH models. These results are supported by the use of robust loss functions and the Hansen's (2005) superior predictive ability test. The improvement in forecasting accuracy of oil price return volatility based on the nonparametric GARCH model suggests that this method offers an attractive and viable alternative to the commonly used parametric GARCH models.