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This paper introduces the $\sigma$-Cell, a novel Recurrent Neural Network(RNN) architecture for financial volatility modeling. Bridging traditionaleconometric approaches like GARCH with deep learning, the $\sigma$-Cellincorporates stochastic layers and time-varying parameters to capture dynamicvolatility patterns. Our model serves as a generative network, approximatingthe conditional distribution of latent variables. We employ alog-likelihood-based loss function and a specialized activation function toenhance performance. Experimental results demonstrate superior forecastingaccuracy compared to traditional GARCH and Stochastic Volatility models, makingthe next step in integrating domain knowledge with neural networks.

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