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Structured SDEs for Realized GARCH: Continuous-Time Volatility Modelling and Component-Level Analysis

Hongyu Yao, Zhengyang Chi, Junbin Gao · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.17732 · cited by 0 works (OpenAlex) · open-access PDF

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Proponemos un modelo estructurado de volatilidad estocástica de tiempo continuo para la predicción de variación integrada de un día. El modelo introduce un estado de medida realizado conjuntamente que se alimenta directamente en la dinámica de variación latente, mientras que las innovaciones de Brownian correlacionadas capturan la dependencia relacionada con el retorno. Los parámetros se estiman a través de aprendizaje predictivo basado en simulaciones, y la simulación de Monte Carlo predice la variación integrada. A través de 17 índices de acciones, el modelo propuesto muestra un fuerte desempeño fuera de muestra en relación con GARCH, GARCH-Itô, Realized GARCH, HAR, y HEAVY en los parámetros de referencia de QLIKE, MSE, y MAE. Los resultados de la

Machine translation (Meta M2M100); the English original follows.

Abstract

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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Topics: Stochastic volatility, Volatility (finance), Econometrics, Monte Carlo method, Realized variance, Computer science

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