Machine Learning Applications in Empirical Finance: Volatility Modeling and Forecasting

Predicting volatility in financial markets is crucial for assessing financial risks. While deep learning has significantly progressed, neural networks often require additional features to outperform traditional econometric models for volatility prediction. It could be due to complexities such as market noise, microstructure, heteroscedasticity, news effects, and multiple time scales. Although econometric models for price volatility have evolved considerably over the years, the potential for integrating these models with deep learning techniques, particularly Recurrent Neural Networks (RNNs), still needs to be explored.In this research, we investigate the performance of Long Short-Term Memory (LSTM) RNNs in predicting volatility and benchmark performance against established econometric models. Specifically, we investigate the impact of hyperparameter optimization, focusing on input dimension and LSTM architecture.We introduce a novel RNN cell design called the σ-Cell to address the challenges of volatility modeling within deep learning. This design incorporates domain-specific knowledge and time-varying parameters, resulting in a generative network that captures the joint distribution of the stochastic volatility process. It also provides an approximation of the conditional distribution of latent variables. We employ a log-likelihood-based loss function to optimize the model and introduce a specialized Adjusted-Softplus activation function.Furthermore, we propose a new LSTM cell variant, σ-LSTM, including a stochastic processing layer. By embedding stylized facts related to volatility as a form of inductive bias, we improve the model's predictive accuracy by utilizing a probabilistic loss function.Our research underscores the value of integrating domain knowledge with deep learning techniques for more accurate volatility prediction in financial markets. It also emphasizes the importance of meticulous hyperparameter tuning, particularly concerning input dimension and architecture.