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Structured SDEs for Realized GARCH: Continuous-Time Volatility 模型 (Model)ling and Component-Level 分析 (Analysis)
Structured SDEs for Realized GARCH: Continuous-Time Volatility Modelling and Component-Level Analysis

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We propose a structured continuous-time stochastic volatility model for one-day-ahead integrated-variance forecasting. The model introduces a jointly evolving realized-measure state that feeds directly into latent variance dynamics, while correlated Brownian innovations capture return-linked dependence. Parameters are estimated through simulation-based predictive learning, and Monte Carlo simulation forecasts integrated variance. Across 17 equity indices, the proposed model shows strong out-of-sample performance relative to GARCH, GARCH-Itô, Realized GARCH, HAR, and HEAVY benchmarks under QLIKE, MSE, and MAE. Ablation results show that realized-measure feedback provides substantial incremental forecasting value within the proposed framework, while return-linked Brownian dependence contributes more modest complementary gains. The results support incorporating measurement-driven information directly into continuous-time latent volatility dynamics to improve integrated-variance forecasting.

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