Monte Carlo Approaches for calculating Value-at-Risk (VaR) are powerful tools widely used by financial risk managers across the globe. However, they are time consuming and sometimes inaccurate. In this paper, a fast and accurate Monte Carlo algorithm for calculating VaR and ES based on Gaussian Mixture Models is introduced. Gaussian Mixture Models are able to cluster input data with respect to market’s conditions and therefore no correlation matrices are needed for risk computation. Sampling from each cluster with respect to their weights and then calculating the volatility-adjusted stock returns leads to possible scenarios for prices of assets. Our results on a sample of US stocks show that the Gmm-based VaR model is computationally efficient and accurate. From a managerial perspective, our model can efficiently mimic the turbulent behavior of the market. As a result, our VaR measures before, during and after crisis periods realistically reflect the highly non-normal behavior and non-linear correlation structure of the market.

用于计算风险价值 (VaR) 的蒙特卡罗方法是全球金融风险管理人员广泛使用的强大工具。但是，它们很耗时，有时不准确。本文介绍了一种基于高斯混合模型计算VaR和ES的快速准确的蒙特卡罗算法。高斯混合模型能够根据市场条件对输入数据进行聚类，因此风险计算不需要相关矩阵。根据权重从每个集群中抽样，然后计算经波动率调整的股票收益，得出资产价格的可能情景。我们对美国股票样本的结果表明，基于 Gmm 的 VaR 模型在计算上是高效且准确的。从管理的角度来看，我们的模型可以有效地模拟市场的动荡行为。因此，我们在危机之前、期间和之后的 VaR 衡量标准真实地反映了市场的高度非正常行为和非线性相关结构。