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

Paper: arXiv 2610.17732

Authors: Hongyu Yao, Zhengyang Chi, Junbin Gao

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel continuous-time stochastic volatility model incorporating realized measures, demonstrating strong empirical performance across multiple equity indices. The mathematical framework is sophisticated, involving SDEs and simulation-based learning, while the empirical validation is thorough and comparative.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve One-Day-Ahead Integrated Variance Forecasting] --> B{Proposed Model: Structured Continuous-Time SDE for Realized GARCH};
    B --> C[Data/Inputs: 17 Equity Indices];
    C --> D{Methodology: Simulation-based Predictive Learning for Parameters, Monte Carlo for Forecasting};
    D --> E[Computational Processes: Model Estimation, Integrated Variance Forecasting];
    E --> F{Key Outcomes: Strong Out-of-Sample Performance, Realized-Measure Feedback Provides Substantial Value};
    F --> G[Conclusion: Incorporating Measurement-Driven Information Improves Forecasting];