Jump Volatility Forecasting for Crude Oil Futures Based on Complex Network and Hybrid CNN–Transformer Model

The crude oil futures market is highly susceptible to policy changes and international relations, which often trigger abrupt jumps in prices. The existing literature rarely considers jump volatility and the underlying impact mechanisms. This study proposes a hybrid forecasting model integrating a convolutional neural network (CNN) and self-attention (Transformer) for high-frequency financial data, based on the complex network characteristics between trading information and multi-market financialization indicators. Empirical results demonstrate that incorporating complex network indicators enhances model performance, with the CNN–Transformer model with a complex network achieving the highest predictive accuracy. Furthermore, we verify the model’s effectiveness and robustness in the WTI crude oil market via Diebold–Mariano tests and external event shock. Notably, this study also extends the analytical framework to jump intensity, thereby providing a more accurate and robust jump forecasting model for risk management and trading strategies in the crude oil futures market.