Structured Continuous-Time SDEs Improve Realized GARCH Integrated-Variance Forecasting

01 ABSTRACT

The authors propose a structured continuous-time stochastic volatility model for one-day-ahead integrated-variance forecasting, where a jointly evolving realized-measure state feeds directly into latent variance dynamics and correlated Brownian innovations capture return-linked dependence. Parameters are estimated via simulation-based predictive learning, and forecasts are generated by Monte Carlo simulation. The authors report strong out-of-sample performance against GARCH, GARCH-It^o, Realized GARCH, HAR and HEAVY benchmarks on 17 equity indices, with ablation showing substantial incremental value from realized-measure feedback and more modest gains from return-linked Brownian dependence; these findings are the authors' reports under their specific setup and dataset and require independent verification.

02 KEY FINDINGS

1. The model introduces a realized-measure state that jointly evolves with latent variance in continuous time, and uses correlated Brownian innovations to capture return-linked dependence.
2. It targets one-day-ahead integrated variance, estimates parameters through simulation-based predictive learning, and generates forecasts via Monte Carlo simulation.
3. On 17 equity indices, it outperforms GARCH, GARCH-It^o, Realized GARCH, HAR and HEAVY benchmarks under QLIKE, MSE and MAE; ablation indicates realized-measure feedback adds more incremental value than return-linked Brownian dependence.