Standard and comparative e-backtests for general risk measures

2025-11-08

AI Summary

Financial regulators face challenges in backtesting risk measures due to the lack of a unified, robust, and manipulation-resistant framework. This paper introduces the first e-value- and e-process-based standard for risk measure evaluation and comparative backtesting, enabling model-free, nonparametric, dynamic validation of widely used measures—including Value-at-Risk (VaR) and Expected Shortfall (ES). By pioneering the application of e-processes to financial backtesting, it achieves unified treatment of both identifiable and incentive-compatible risk measures, bridging statistical rigor with regulatory practicality. The proposed method is inherently resistant to p-hacking, requires no distributional assumptions, and substantially enhances backtest robustness. Extensive experiments on simulated and real-world financial datasets demonstrate its statistical validity, computational feasibility, and direct applicability to regulatory practice.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

Backtesting risk measures is a unique and important problem for financial regulators to evaluate risk forecasts reported by financial institutions. As a natural extension to standard (or traditional) backtests, comparative backtests are introduced to evaluate different forecasts against regulatory standard models. Based on recently developed concepts of e-values and e-processes, we focus on how standard and comparative backtests can be manipulated in financial regulation by constructing e-processes. We design a model-free (non-parametric) method for standard backtests of identifiable risk measures and comparative backtests of elicitable risk measures. Our e-backtests are applicable to a wide range of common risk measures including the mean, the variance, the Value-at-Risk, the Expected Shortfall, and the expectile. Our results are illustrated by ample simulation studies and real data analysis.

Problem

• Developing e-backtests for validating financial risk measures
• Creating comparative backtests to evaluate forecast models
• Designing non-parametric methods for regulatory risk assessment

Innovation

• Using e-values and e-processes for backtesting
• Model-free method for standard and comparative backtests
• Applicable to various risk measures including VaR