Reliable value at risk estimation with conformal prediction

Abstract

Value-at-Risk (VaR), the most widely used measure of market risk, is typically evaluated through backtesting of point forecasts. Such procedures, however, say little about the uncertainty of the estimated quantile. Existing interval methods are each tied to a specific model class and fail when its underlying assumptions are violated. We propose Quantile Dynamically-Tuned Adaptive Conformal Inference (QDtACI), a model-agnostic conformal calibration layer that constructs finite-sample intervals around any VaR forecast, using only the return series and the forecast itself. QDtACI adapts dynamically-tuned adaptive conformal inference to the quantile setting through two components: a pinball-loss nonconformity score aligned with the quantile objective and an asymmetric interval construction, and a multi-speed expert-aggregation mechanism driven by a smoothed violation error and a composite loss on coverage, width, and stability. On synthetic GARCH data, where the true VaR is observable, QDtACI attains near-nominal coverage of the true VaR when the underlying forecast is well-specified, and its coverage degrades in a controlled way as the forecast is misspecified. Against the Delta method, a bootstrap, and the DtACI baseline, it achieves coverage closer to nominal at comparable or better interval quality (Winkler score). Applied to a portfolio of 24 fixed-income assets (2016–2024) with VaR forecasts from CAViaR, DCC-GARCH, and copula models, the intervals are stable in calm periods and widen sharply during stress, including the COVID-19 shock and the 2022–2023 monetary tightening. Because true coverage cannot be measured on real data, we further provide a return-only diagnostic that indicates when interval calibration can be trusted as a proxy for coverage of the true VaR. QDtACI thus offers a single, broadly applicable procedure for uncertainty quantification in VaR, whose reliability tracks the quality of the underlying forecast.