AbstractFrom the cross‐market perspective, this paper investigates crude oil volatility index (OVX) forecasts by proposing a hybrid method, which combines the data‐driven SVR technique and parametric models. In terms of parametric models, we utilize GARCH‐type models with jumps, and the forecasting effects of five non‐parametric jumps (including interday and intraday jump tests) of stock market are also explored. Empirical results show that our approach can substantially increase forecasting accuracy. In addition, the model confidence set test and robust test reaffirm the superiority of the novel hybrid method. From the assessment of economic significance, the advantages of the hybrid method for volatility index forecasting are further confirmed. All these findings imply that jumps of stock market can be helpful in forecasting OVX, especially after the introduction of the hybrid method. Our work can certainly provide a new insight for volatility forecasting and cross‐market research.