Risk management is an important part of financial practice, essential for protecting assets and investments in modern-day volatile markets. This paper proposes a mixture of mirrored Weibull (MMW) distribution for modelling stock returns and estimating risk measures. Unlike common practices which are typically based on the normal distribution, the MMW model can flexibly accommodate non-normal features frequently exhibited in financial data. It also enjoys appealing properties such as having a simple density expression and fast parameter estimation. We demonstrate the effectiveness of our model by assessing its performance in Value-at-Risk (VaR) estimation of three S&P500 stocks. The MMW model compares favourably to Gaussian mixture model and t-mixture model, with significant improvements in VaR estimation and prediction.

翻译：风险管理是金融实践的重要组成部分，对于在现代波动性市场中保护资产和投资至关重要。本文提出一种混合镜像威布尔分布（MMW）模型，用于建模股票收益率并估计风险度量。与通常基于正态分布的常见做法不同，MMW模型能够灵活适应金融数据中频繁出现的非正态特征。该模型还具有密度表达式简单、参数估计快速等优良性质。我们通过评估其在三只标普500股票风险价值（VaR）估计中的表现，论证了模型的有效性。与高斯混合模型和t混合模型相比，MMW模型在VaR估计和预测方面展现出显著优势。