Volatility-inspired $\sigma$-LSTM cell

TL;DR

This paper introduces a novel $\sigma$-LSTM cell that incorporates volatility process knowledge as an inductive bias, enhancing neural network performance in volatility forecasting.

Contribution

It proposes a new $\sigma$-LSTM cell with a stochastic layer, integrating volatility physics into neural network architecture for improved forecasting.

Findings

Good out-of-sample forecasting performance

Effective incorporation of volatility physics as inductive bias

Novel stochastic processing layer in LSTM

Abstract

Volatility models of price fluctuations are well studied in the econometrics literature, with more than 50 years of theoretical and empirical findings. The recent advancements in neural networks (NN) in the deep learning field have naturally offered novel econometric modeling tools. However, there is still a lack of explainability and stylized knowledge about volatility modeling with neural networks; the use of stylized facts could help improve the performance of the NN for the volatility prediction task. In this paper, we investigate how the knowledge about the "physics" of the volatility process can be used as an inductive bias to design or constrain a cell state of long short-term memory (LSTM) for volatility forecasting. We introduce a new type of $\sigma$-LSTM cell with a stochastic processing layer, design its learning mechanism and show good out-of-sample forecasting performance.