用混合高斯过程模型更稳健地估计股市波动与相关性，适合监管风控场景。
A Hybrid Gaussian Process Regression Framework for Stable Volatility-Covariance Estimation: Evidence from Global Equity Indices
- 分步建模：单资产波动用高斯过程动态拟合，跨资产相关性用历史数据稳定估计
- 在2020年6月到2025年6月测试中，组合预期缺口（ES）100%达标，优于传统方法
- 创新噪声初始化策略确保数值稳定，适合金融监管对保守预测的要求
准确预测波动-协方差矩阵（VCV）是内部资本充足评估流程（ICAAP）和全面资本分析与审查（CCAR）的核心。传统计量模型如GARCH族和指数加权移动平均（EWMA）存在参数刚性、分布假设依赖及压力情境下的数值不稳定性，导致尾部风险系统低估。本文提出并验证了一种新型混合高斯过程回归-历史模拟（GPR-HS）框架，用于估算七大全球主要股指组合的市值风险（VaR）与预期缺口（ES）。该框架解耦VCV估计：采用带Matern 5/2核的单变量高斯过程动态建模各资产波动率，跨资产相关性则通过稳定的历史协方差估计。关键方法贡献为激进噪声初始化（ANI）策略——将初始白噪声核方差设为训练收益率的实证方差，以保证格拉姆矩阵正定性、实现正则化，并生成保守且符合监管要求的预测。基于2020年6月至2025年6月的滚动窗口前向链式交叉验证，该框架在多数测试片段中满足监管要求；组合层面预期缺口（ES）达标率为100%，在71.4%的单变量情形下，二次损失优于静态历史法，且所有情形下违约次数均更低。
原文摘要 · Abstract (English)
Accurate forecasting of the Volatility-Covariance Matrix (VCV) is central to regulatory capital adequacy processes such as the Internal Capital Adequacy Assessment Process (ICAAP) and the Comprehensive Capital Analysis and Review (CCAR). Traditional econometric models, including GARCH-family and Exponentially Weighted Moving Average (EWMA) approaches, suffer from parametric rigidity, distributional assumptions, and numerical instability under stress, leading to systematic underestimation of tail risk. This paper proposes and validates a novel Hybrid Gaussian Process Regression-Historical Simulation (GPR-HS) framework for estimating Value-at-Risk (VaR) and Expected Shortfall (ES) across a diversified portfolio of seven major global equity indices. The framework decouples the VCV estimation problem: individual asset volatilities are modelled dynamically using Univariate GPR with a Matern 5/2 kernel, while inter-asset correlations are estimated via stable historical covariance. A key methodological contribution is the Aggressive Noise Initialization (ANI) strategy, which sets the initial White Noise kernel variance equal to the empirical variance of the training returns, ensuring Gram matrix positive-definiteness, regularization, and conservative, regulatory-compliant forecasts. Evaluated using an expanding window forward-chaining cross-validation scheme over June 2020 -June 2025, the GPR-HS framework achieves regulatory compliance in the majority of test splits; including a 100% ES pass rate at the portfolio level, while outperforming the static Historical VaR benchmark in 71.4% of univariate cases by Quadratic Loss and 100% of cases by violation count.
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