Isotonic recalibration under a low signal-to-noise ratio

Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to restore auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to an explainable pricing system because the resulting isotonically recalibrated regression function has a low complexity.