Introducing the $σ$-Cell: Unifying GARCH, Stochastic Fluctuations and Evolving Mechanisms in RNN-based Volatility Forecasting

ArXiv ID: 2309.01565 “View on arXiv”

Authors: Unknown

Abstract

This paper introduces the $σ$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $σ$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating domain knowledge with neural networks.

Keywords: Recurrent Neural Network (RNN), volatility modeling, GARCH, generative network, stochastic layers, Equity (Stock)

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper introduces a novel RNN architecture with stochastic layers and time-varying parameters, requiring advanced stochastic calculus and deep learning theory, yet backs its claims with multiple real-world datasets (S&P 500, BTC-USD) and comparative benchmarks against established econometric models.
  flowchart TD
    A["Research Goal:<br>Develop a neural architecture<br>unifying GARCH & RNN for<br>financial volatility forecasting"] --> B["Methodology:<br>Introduce σ-Cell RNN<br>with stochastic layers &<br>time-varying parameters"]
    B --> C["Data & Inputs:<br>Equity (Stock) returns<br>historical volatility data"]
    C --> D["Computational Process:<br>Generative network approximating<br>conditional distribution via<br>log-likelihood loss function"]
    D --> E["Outcomes:<br>Superior forecasting accuracy<br>vs. GARCH/SV models<br>Successful integration of<br>domain knowledge & neural networks"]