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

By Hongyu Yao, Zhengyang Chi, Junbin Gao

Rating

1809
Battle Count: 53

Relevance

8/10
Highly relevant for risk management and options pricing where accurate integrated variance forecasts are critical. The continuous-time framework allows for more granular modeling of volatility dynamics compared to discrete GARCH, though computational cost is higher.

Implementation Complexity

8/10
Requires implementing SDE solvers (Euler-Maruyama), Monte Carlo simulation for both estimation and forecasting, and handling correlated Brownian motions. The use of torchsde and Adam optimizer suggests a deep learning-adjacent implementation stack.

Reproducibility

5/5
The paper provides a public GitHub repository link (https://github.com/Haley-xixi/realized-garch-sde-code). The data source (WRDS) is specified, and while WRDS is subscription-based, the methodology and code are fully open, and the paper details the exact preprocessing and evaluation protocols.

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.

Links

arXiv:2610.17732 · Code · Paper rankings

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