A compensatory model for quantile estimation and application to VaR

Abstract

Unlike the standard two-step workflow of estimating a time series distribution and extracting quantiles from it, this paper proposes a compensatory model to refine quantile estimates based on an existing fitted distribution. We embed a new penalty term in the model and theoretically characterize its ability to bound realized coverage errors, yielding an adaptive quantile estimator. Backtests on the S&P 500 and NASDAQ Composite show that the compensatory model substantially reduces unconditional coverage errors across four VaR estimators: all 16 compensatory model forecasts pass the unconditional coverage test, compared with 7 of the 16 corresponding Base forecasts. The conditional-calibration results remain estimator-dependent, indicating that compensatory model is a coverage-correction layer rather than a replacement for conditional-tail modelling.

10 pages, 1 figures