Forecasting Probability Distributions of Financial Returns with Deep Neural Networks
This work provides a viable deep learning alternative for financial risk assessment and portfolio management, though it is incremental as it applies existing methods to financial data.
This study tackled forecasting probability distributions of financial returns using deep neural networks, finding that LSTM with skewed Student's t distribution performed best across multiple criteria, capturing heavy tails and asymmetry and competing with classical GARCH models for Value-at-Risk estimation.
This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.