Calibrated quantile prediction for Growth-at-Risk

TL;DR

This paper introduces a conformal framework for calibrated extremal quantile estimation, significantly improving the accuracy and robustness of risk measures like Growth-at-Risk, especially at extreme quantiles critical for financial risk management.

Contribution

The work presents a new conformal prediction method for extremal quantiles, ensuring better calibration and coverage guarantees in risk assessment applications.

Findings

Consistent improvement in calibration and robustness of quantile estimates.

Enhanced accuracy at extremal quantiles critical for risk management.

Introduction of a property guaranteeing coverage under exchangeability.

Abstract

Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are particularly critical in calculating risk measures, such as Growth-at-Risk (GaR). % and Value-at-Risk (VaR). This work proposes a conformal framework to estimate calibrated quantiles, and presents an extensive simulation study and a real-world analysis of GaR to examine its benefits with respect to the state of the art. Our findings show that CP methods consistently improve the calibration and robustness of quantile estimates at all levels. The calibration gains are appreciated especially at extremal quantiles, which are critical for risk assessment and where traditional methods tend to fall short. In addition, we introduce a novel property that guarantees coverage under the exchangeability assumption, providing a valuable tool for managing risks by quantifying and controlling the likelihood of future extreme observations.