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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

Japanese

私たちは、一日前の統合変動予測のための構造化された継続的ストーカスティック変動性モデルを提案します。このモデルは、隠れた変動性ダイナミクスに直接フィードする共に進化する実現測定状態を導入しますが、関連するブラウニアのイノベーションは、リターン関連の依存性をキャプチャします。パラメータはシミュレーションベースの予測学習を通じて推定され、モンテカルロのシミュレーションは統合変動性を予測します。17の株式インデックスを超えて、提案されたモデルは、GARCH、GARCH-Itô、Realized GARCH、HAR、およびHEAVYベンチャー基準の基準に比

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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