使用深度神經網路預測金融回報的機率分佈

Forecasting Probability Distributions of Financial Returns with Deep Neural Networks

August 26, 2025

作者: Jakub Michańków

cs.AI

摘要

本研究評估了深度神經網絡在預測金融收益概率分佈方面的應用。研究採用一維卷積神經網絡（CNN）和長短期記憶（LSTM）架構來預測三種概率分佈的參數：正態分佈、學生t分佈和偏態學生t分佈。通過自定義的負對數似然損失函數，直接優化分佈參數。模型在六個主要股票指數（標普500、巴西BOVESPA、德國DAX、波蘭WIG、日經225和韓國KOSPI）上進行測試，並使用概率評估指標，包括對數預測分數（LPS）、連續排序概率分數（CRPS）和概率積分變換（PIT）。結果表明，深度學習模型提供了準確的分佈預測，並在風險價值（VaR）估計方面與傳統的GARCH模型表現相當。其中，採用偏態學生t分佈的LSTM模型在多個評估標準中表現最佳，能夠捕捉金融收益的厚尾特性和不對稱性。這項工作表明，深度神經網絡是金融風險評估和投資組合管理中傳統計量經濟模型的可行替代方案。

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.