A hybrid value-at-risk/estimated shortfall model: linking accuracy, calibration and explanation stability across horizons

Zhixing Lin and Yu Xia

Abstract

Machine learning offers improved forecasting accuracy for financial risk models, yet regulated institutions increasingly require governance-grade evidence that goes beyond traditional backtesting. We identify a deployability gap: existing hybrid approaches maximize predictive performance but leave the auditability question unanswered. To close this gap, we propose an auditable hybrid quantile framework that anchors nonlinear gradient boosting corrections to a linear heterogeneous autoregressive volatility baseline, enabling validators to separately audit the economically motivated baseline and the machine learning adjustment. The framework is evaluated using strict walk-forward validation across eight major global equity indexes, with crisis subsamples covering the global financial crisis and the Covid-19 pandemic. We find that the hybrid architecture delivers its largest accuracy gains at multiweek regulatory horizons, where structural nonlinearities matter most. Tail-risk calibration, assessed through Basel III traffic light backtests and Fissler–Ziegel joint value-at-risk–expected shortfall scoring, improves consistently relative to both the econometric baseline and a pure machine learning benchmark. Explanation stability, quantified via a model governance scorecard, remains high under rolling reestimation, providing auditable evidence that the model relies on economically coherent drivers rather than transient noise. The framework is designed to be compatible with the use-test requirements of the Fundamental Review of the Trading Book, supporting deployment in governance-sensitive risk environments.