Taming Tail Risk: Regime-Weighted Conformal Calibration for Nonstationary Value-at-Risk

Marc Schmitt

Papers from arXiv.org

Abstract: Value-at-risk (VaR) forecasts drive trading constraints and capital allocation, yet realized exceedance rates concentrate in stress periods, when losses are largest. This paper studies sequential one-sided VaR calibration via conformal prediction. Regime-weighted conformal calibration (RWC) wraps any quantile forecaster and calibrates an additive safety buffer from past forecast errors, weighted by exponential time decay and regime similarity computed from simple market features; time-weighted calibration (TWC) is the kernel-free special case. Rather than assuming weighted exchangeability with respect to the algorithm's own weights, the coverage gap is bounded for arbitrary data-driven weights by conditioning on the regime path and exploiting total-variation smoothness of the score distribution across regimes and time. On the CRSP value-weighted index and sixteen CRSP-derived equity portfolios (1990--2024), RWC is benchmarked against adaptive conformal inference, DtACI, and conformal PID control at the Basel-relevant 99% and 97.5% levels. Time-decay calibration is a strong default under drift; regime weighting improves stress-regime calibration when the base forecaster adapts slowly and tightens bounds when it does not, and effective-sample-size diagnostics indicate when localization is reliable.

Date: 2026-02, Revised 2026-07
New Economics Papers: this item is included in nep-fmk, nep-for and nep-rmg
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