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];

Cited References (78)

  1. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation (1982)
  2. A Correlated Stochastic Volatility Model Measuring Leverage and Other Stylized Facts (2002) — link
  3. The Leverage Effect Puzzle under Semi-nonparametric Stochastic Volatility Models (2024) — link
  4. Estimating Stochastic Volatility Models Using Realized Measures (2016) — link
  5. Strictly Proper Scoring Rules, Prediction, and Estimation (2007) — link
  6. Testing the Equality of Prediction Mean Squared Errors (1997) — link
  7. The Stationary Bootstrap (1994) — link
  8. Tests of Conditional Predictive Ability (2006) — link
and 70 more
  1. Maximum Likelihood Estimation of Misspecified Models (1982)
  2. Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances (1992)
  3. Realized Stochastic Volatility with Leverage and Long Memory (2014) — link
  4. Monte Carlo Methods in Financial Engineering (2004)
  5. Numerical Solution of Stochastic Differential Equations (1992)
  6. Generalized Autoregressive Conditional Heteroskedasticity (1986)
  7. Automatic Lag Selection in Covariance Matrix Estimation (1994)
  8. A New Approach to Linear Filtering and Prediction Problems (1960)
  9. Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models (2002) — link
  10. Modeling and Forecasting Realized Volatility (2003) — link
  11. Forecasting stock market volatility: Further international evidence (2006)
  12. Multilevel Monte Carlo Simulation for the Heston Stochastic Volatility Model (2023) — link
  13. Adam: A Method for Stochastic Optimization (2015)
  14. Modelling Volatility Cycles: The MF2-GARCH Model (2025) — link
  15. An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations (2001) — link
  16. Efficient and Accurate Gradients for Neural SDEs (2021)
  17. New Results in Linear Filtering and Prediction Theory (1961)
  18. A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix (1987)
  19. Deep Kalman Filters (2015)
  20. Time Series Analysis by State Space Methods (2012)
  21. Volatility forecast comparison using imperfect volatility proxies (2011)
  22. Comparing predictive accuracy (1995)
  23. A forecast comparison of volatility models: Does anything beat a Garch (1,1)? (2005)
  24. Asymptotic inference about predictive ability (1996)
  25. Discretization of Processes (2012)
  26. Closed-form likelihood expansions for multivariate diffusions (2008)
  27. Unified Discrete-Time and Continuous-Time Models and Statistical Inferences for Merged Low-Frequency and High-Frequency Financial Data (2016)
  28. Augmented GARCH $(p,q)$ Process and Its Diffusion Limit (1997) — link
  29. ARCH Models as Diffusion Approximations (1990) — link
  30. Realising the Future: Forecasting with High-Frequency-Based Volatility ( HEAVY ) Models (2010) — link
  31. A Simple Approximate Long-Memory Model of Realized Volatility (2009) — link
  32. Estimating Quadratic Variation Using Realized Variance (2002) — link
  33. The Distribution of Realized Exchange Rate Volatility (2001) — link
  34. Roughing it up: Including jump components in the measurement of return volatility (2007)
  35. Neural controlled differential equations for irregular time series (2020)
  36. Studies of stock price volatility changes (1976)
  37. Forecasting: Principles and Practice (2021) — link
  38. Deep Learning (2016) — link
  39. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models (2002)
  40. The relative contribution of jumps to total price variance (2005)
  41. Numerical Solution of Stochastic Differential Equations (1992)
  42. Numerical Solution of Stochastic Differential Equations with Jumps in Finance (2010)
  43. Numerical Solution of Stochastic Differential Equations with Jumps in Finance (2007)
  44. Scalable gradients for stochastic differential equations (2020)
  45. Stochastic volatility: Likelihood inference and comparison with ARCH models (1998)
  46. Adam: A method for stochastic optimization (2015)
  47. Continuous-time GARCH processes (2006)
  48. Realized GARCH : A joint model for returns and realized measures of volatility (2012)
  49. Stochastic Volatility: Selected Readings (2023)
  50. Volatility analysis with realized GARCH-It ^o models (2021)
  51. Stochastic Volatility and Realized Stochastic Volatility Models (2023)
  52. On stochastic differential equations (1951)
  53. Option pricing when underlying stock returns are discontinuous (1976)
  54. Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues (2001)
  55. The microstructure of stochastic volatility models with self-exciting jump dynamics (2022)
  56. A comparative analysis of stochastic models for stock price forecasting: The influence of historical data duration and volatility regimes (2025)
  57. On the difficulty of training recurrent neural networks (2013)
  58. Efficient and Accurate Gradients for Neural SDE s (2021)
  59. Convergence and stability analysis of neural stochastic differential equations with Poisson jumps (2026)
  60. Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling (2014)
  61. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  62. Power and bipower variation with stochastic volatility and jumps (2004)
  63. A theory of the term structure of interest rates (1985)
  64. A long short-term memory enhanced realized conditional heteroskedasticity model (2025)
  65. Stable neural stochastic differential equations in analyzing irregular time series data (2024)
  66. Integrated OU Processes and Non - Gaussian OU - Based Stochastic Volatility Models (2003) — link
  67. Nonlinear Systems (2002)
  68. The Model Confidence Set (2011)
  69. Stochastic Differential Equations: An Introduction with Applications (2003)
  70. Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data (2025) — link

0 of 78 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.