Paper: arXiv 2410.00288

Abstract

Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE).

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts such as GARCH model formulations and deep learning architectures with LSTM, indicating high mathematical density. It demonstrates strong empirical rigor through rigorous backtesting on multiple global indices, using standard error metrics like R2, MSE, and MAE, and provides detailed methodology for implementation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Predict Financial Volatility<br>More Accurately"] --> B["Key Inputs<br>Time Series Data"]
  B --> C["GARCH-Informed Neural Network (GINN)<br>Hybrid Methodology"]
  C --> D["GARCH Module<br>Captures Stylized Facts"]
  C --> E["LSTM Module<br>Deep Learning Flexibility"]
  D --> F["Computation<br>Physics-Informed Training"]
  E --> F
  F --> G["Key Outcomes<br>Superior Forecast Accuracy"]
  G --> H["Metrics<br>R² ↑ | MSE ↓ | MAE ↓"]

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0 of 44 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.