Rapidly evolving market conditions call for real-time risk monitoring, but its online estimation remains challenging. In this paper, we study the online estimation of one of the most widely used risk measures, Value at Risk (VaR). Its accurate and reliable estimation is essential for timely risk control and informed decision-making. We propose to use the quantile regression forest in the offline-simulation-online-estimation (OSOA) framework. Specifically, the quantile regression forest is trained offline to learn the relationship between the online VaR and risk factors, and real-time VaR estimates are then produced online by incorporating observed risk factors. To further ensure reliability, we develop a conformalized estimator that calibrates the online VaR estimates. To the best of our knowledge, we are the first to leverage conformal calibration to estimate real-time VaR reliably based on the OSOA formulation. Theoretical analysis establishes the consistency and coverage validity of the proposed estimators. Numerical experiments confirm the proposed method and demonstrate its effectiveness in practice.

翻译：快速变化的市场条件要求实时风险监控，但其在线估计仍具挑战性。本文研究最广泛使用的风险度量之一——风险价值（VaR）的在线估计。其准确可靠的估计对于及时风险控制和明智决策至关重要。我们提出在离线模拟-在线估计（OSOA）框架中使用分位数回归森林。具体而言，分位数回归森林在离线阶段训练以学习在线VaR与风险因子之间的关系，随后在线阶段通过结合观测到的风险因子生成实时VaR估计。为进一步确保可靠性，我们开发了一种保形化估计器，用于校准在线VaR估计。据我们所知，我们是首个基于OSOA框架利用保形校准实现可靠实时VaR估计的研究。理论分析证明了所提估计器的一致性与覆盖有效性。数值实验验证了所提方法，并展示了其在实际应用中的有效性。