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Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration

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

TL;DR

The paper tackles real-time Value at Risk (VaR) estimation under online risk monitoring using the OSOA framework. It combines offline training of a Quantile Regression Forest (QRF) to model the conditional VaR with online evaluation and introduces conformal calibration to guarantee coverage, yielding both consistency and finite-sample reliability guarantees. Theoretical results establish pointwise and L^2 consistency for the QRF estimator and finite-sample marginal coverage for the conformal QRF, with asymptotic conditional coverage under regularity. Numerical experiments on a realistic options portfolio demonstrate improved reliability (lower miscalibration) and competitive accuracy, validating the approach for practical risk management.

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.

Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration

TL;DR

The paper tackles real-time Value at Risk (VaR) estimation under online risk monitoring using the OSOA framework. It combines offline training of a Quantile Regression Forest (QRF) to model the conditional VaR with online evaluation and introduces conformal calibration to guarantee coverage, yielding both consistency and finite-sample reliability guarantees. Theoretical results establish pointwise and L^2 consistency for the QRF estimator and finite-sample marginal coverage for the conformal QRF, with asymptotic conditional coverage under regularity. Numerical experiments on a realistic options portfolio demonstrate improved reliability (lower miscalibration) and competitive accuracy, validating the approach for practical risk management.

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.
Paper Structure (8 sections, 4 theorems, 37 equations, 3 figures)

This paper contains 8 sections, 4 theorems, 37 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Formulation
  4. The QRF Estimator
  5. The Conformal QRF Estimator
  6. Theoretical Guarantees
  7. Numerical Experiments
  8. Conclusion

Key Result

Theorem 1

Under Assumptions 1--5, for any $\mathbf{x}\in \mathcal{X}$, the proposed online estimator for VaR with confidence level $\alpha$ satisfies where $n$ is the offline sample size.

Figures (3)

  • Figure 1: MRISE of QRF (left) and Conformal QRF (right) under varying offline sample sizes and quantile levels.
  • Figure 2: MPL of QRF (left) and Conformal QRF (right) under varying offline sample sizes and quantile levels.
  • Figure 3: MCR of QRF and Conformal QRF under varying offline sample sizes and quantile levels.

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Proposition 1
  • Theorem 3
  • proof