Compensatory model for quantile estimation and application to VaR

TL;DR

This paper introduces a compensatory model with a novel penalty term to enhance quantile estimation accuracy, particularly improving Value at Risk (VaR) predictions under a fixed distribution estimate.

Contribution

The paper proposes a new compensatory model with a penalty term that controls convergence error and adaptively adjusts quantile estimates, improving VaR performance.

Findings

Significant improvement in VaR estimation accuracy

The penalty term effectively controls convergence error

Adaptive quantile estimation enhances risk assessment

Abstract

In contrast to the usual procedure of estimating the distribution of a time series and then obtaining the quantile from the distribution, we develop a compensatory model to improve the quantile estimation under a given distribution estimation. A novel penalty term is introduced in the compensatory model. We prove that the penalty term can control the convergence error of the quantile estimation of a given time series, and obtain an adaptive adjusted quantile estimation. Simulation and empirical analysis indicate that the compensatory model can significantly improve the performance of the value at risk (VaR) under a given distribution estimation.