Forecasting oil price volatility is considered of major importance for numerous stakeholders, including, policy makers, industries, and investors. This paper examines and evaluates the main factors that oil price volatility forecasters should consider before constructing their forecasting models. Such factors are related to (i) direct versus iterated forecasts, (ii) the incorporation of continuous and jump components, (iii) the importance of semi variance volatility measures, and (iv) ordinary least squares (OLS) versus time‐varying parameter (TVP) estimation procedures. We evaluate the performance of these factors for both the realized and implied volatility measures of the West Texas Intermediate (WTI) crude oil price, based on statistical loss functions, as well as their economic use. The results show that depending on whether end users are interested in forecasting the realized or the implied volatility, the factors influencing the accuracy of forecasts are different. In particular, for the realized volatility, direct forecasting based on TVP estimation procedure, as well as using the information obtained in the semi variance measures, is capable of producing significantly superior forecasts. By contrast, separating the continuous and the jump components of the realized volatility does not provide any added value to these forecasts. Turning to the oil price implied volatility index (OVX), based on the economic evaluation of our forecasts, the TVP estimation procedure seems to perform better. In addition, we find evidence that the continuous component and the semivariance measures of the realized volatility also yield better OVX forecasts in the longer run horizons.