Structured SDEs for Realized GARCH: Continuous-Time Volatility Modelling and Component-Level Analysis
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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BibTeX
@misc{yao2026structured,
title = {{Structured SDEs for Realized GARCH: Continuous-Time Volatility Modelling and Component-Level Analysis}},
author = {Hongyu Yao and Zhengyang Chi and Junbin Gao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17732},
eprint = {2610.17732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17732},
}
RIS
TY - UNPB
TI - Structured SDEs for Realized GARCH: Continuous-Time Volatility Modelling and Component-Level Analysis
AU - Hongyu Yao
AU - Zhengyang Chi
AU - Junbin Gao
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17732
UR - https://arxiv.org/abs/2610.17732
AB - 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.
ER -