利用深度神经网络预测金融收益的概率分布

Forecasting Probability Distributions of Financial Returns with Deep Neural Networks

August 26, 2025

作者: Jakub Michańków

cs.AI

摘要

本研究评估了深度神经网络在预测金融收益概率分布方面的应用。采用一维卷积神经网络（CNN）和长短期记忆网络（LSTM）架构，对三种概率分布——正态分布、学生t分布及偏态学生t分布的参数进行预测。通过自定义的负对数似然损失函数，直接优化分布参数。模型在六大主要股票指数（标普500、巴西BOVESPA、德国DAX、波兰WIG、日经225及韩国KOSPI）上进行了测试，并运用了包括对数预测分数（LPS）、连续排名概率分数（CRPS）和概率积分变换（PIT）在内的概率评估指标。结果表明，深度学习模型能够提供精确的分布预测，并在风险价值（VaR）估计方面与传统的GARCH模型表现相当。其中，采用偏态学生t分布的LSTM模型在多项评估标准中表现最佳，有效捕捉了金融收益的厚尾特征与不对称性。此研究证实，深度神经网络可作为传统计量经济学模型在金融风险评估与投资组合管理中的可行替代方案。

English

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.