Paper: arXiv 2602.01912

Authors: Du-Yi Wang, Guo Liang, Kun Zhang, Qianwen Zhu

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper makes an innovative contribution by combining Quantile Regression Forests with conformal prediction under the OSOA framework for real-time VaR estimation. It balances robust theoretical proofs (consistency and coverage validity) with empirical backtesting metrics like pinball loss and root mean squared error.

Research Flowchart

  flowchart TD
    A["<b>Research Goal:</b><br>Reliable Real-Time Value at Risk (VaR) Estimation"] --> B["<b>Inputs:</b><br>Cross-Asset Risk Factors & Offline Simulation"]
    
    subgraph OSOA["Offline-Simulation-Online-Estimation (OSOA) Framework"]
        B --> C["<b>Offline Training:</b><br>Quantile Regression Forest (QRF) learns VaR relationship"]
        C --> D["<b>Online Estimation:</b><br>Generate real-time VaR from observed risk factors"]
        D --> E["<b>Conformal Calibration:</b><br>Calibrate estimates for coverage validity"]
    end

    E --> F["<b>Key Outcomes:</b><br>Proven theoretical consistency, reliable coverage, and effective real-time risk control"]

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1 of 81 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.