Adaptive conformal recalibration of value at risk in market stress windows: hit rates move towards the target on ten models, and the back-tests accept the wrapped runs too easily

None of the eighteen value-at-risk models of a market-risk ladder passes the Kupiec and conditional coverage tests in the 2007 to 2009 window at the 1% or the 2.5% level. We test a wrapper that leaves the model untouched and moves its working tail level each day by a fixed step times the gap between the target and the exceedance indicator, inside a band. On ten models in three stress windows the mean distance of the hit rate from its target falls from 4.02 to 1.83 points, the score changes by at most +4.3%, and the wrapped models pass 45 of 60 cells against 17. These counts are inflated: the update makes the hit count less variable than a binomial count, so a correct wrapped model passes in 99.8% of simulated runs against 92.6% unwrapped at the 1% level. With each count tested against its own null the wrapped models pass 35 cells against 12, and the prediction stated for three models holds in 5 of its 6 cells, not all of them. On known-truth generators the wrapped hit rate is closer to the target in every shifted cell. The coverage guarantee is vacuous at the length of a stress window, and the band limits the repairable scale error (a ratio of 1.75 at 1% for a Student-t model). The expected shortfall stays understated, the delta-normal model gains no window at 1%, and a rolling split-conformal scale passes as many cells with 10 over the score tolerance. Repository and reproducible pipeline (MIT): https://github.com/fsantibanezleal/CAOS_Contraste .