This paper examines tail risk spillovers and cross-market volatility forecasting between the U.S. equity market and the crude oil market. Using realized and implied volatility within a heterogeneous autoregressive (HAR) framework, we document asymmetric and time-varying tail risk transmission across the two markets. Motivated by these findings, we propose several cross-market volatility forecasting strategies, including direct information augmentation, threshold-based designs, forecast averaging, and transfer learning. The results show that incorporating cross-market information improves volatility forecasts primarily at medium and longer horizons, consistent with the forward-looking nature of implied volatility. Moreover, the relative effectiveness of different transmission mechanisms varies across markets, with transfer learning performing particularly well in the crude oil market. Overall, the findings highlight the importance of linking tail risk spillovers to volatility forecasting and demonstrate that flexible cross-market information transmission can enhance predictive performance across markets and horizons.
Péng et al. (Sun,) studied this question.