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

TL;DR

The paper presents the $\sigma$-Cell, a new RNN architecture that combines GARCH, stochastic processes, and evolving mechanisms to improve financial volatility forecasting by capturing dynamic patterns more effectively.

Contribution

It introduces the $\sigma$-Cell, integrating traditional econometric models with deep learning through stochastic layers and time-varying parameters for enhanced volatility prediction.

Findings

Outperforms traditional GARCH and stochastic volatility models in forecasting accuracy.

Incorporates stochastic layers and dynamic parameters for better modeling of volatility.

Uses a generative approach with a specialized loss function for improved performance.

Abstract

This paper introduces the $\sigma$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $\sigma$-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.