A CAR(p)‐Enhanced Jump‐Diffusion Quadratic Rough Heston Model for Financial Volatility Forecasting

ABSTRACT In this paper, we propose a novel approach to volatility forecasting based on an enhanced quadratic rough Heston (QRH) model. The proposed CAR()‐JQRH model integrates jump dynamics, a continuous autoregressive component in the variance process, and a Gamma‐distributed initial variance to better capture volatility persistence, clustering, and abrupt market movements. The model is empirically evaluated using gold futures, crude oil futures, foreign exchange rates, and the SP 500 index. Benchmark comparisons with the standard QRH model show that the proposed framework delivers consistently improved predictive performance across all datasets. These results highlight the flexibility, robustness, and practical relevance of the proposed model for capturing complex volatility dynamics, with potential applications in both forecasting and broader risk management contexts.