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

arXiv: https://arxiv.org/abs/2610.17732 · HTML: https://mlsanity.com/paper/2610.17732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 38 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 2 of 2)

- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Volatility Analysis with Realized GARCH-Ito Models](https://mlsanity.com/paper/1907.01175/) (2019)

## Abstract (arXiv)

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-Ito, 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.