Quantile-based modeling of scale dynamics in financial returns for Value-at-Risk and Expected Shortfall forecasting

TL;DR

This paper presents a semiparametric quantile regression method for forecasting Value-at-Risk and Expected Shortfall by modeling the conditional scale of financial returns, effectively capturing risk dynamics and outperforming traditional models.

Contribution

It introduces a novel distribution-free approach for modeling downside risk in financial returns using restricted quantile regression, improving risk estimation accuracy.

Findings

Method outperforms GARCH and joint quantile models in simulations.

Effective in capturing skewness, heavy tails, and leverage effects.

Demonstrates robustness on international stock index data during COVID-19.

Abstract

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted quantile regression. Focusing on downside risk, VaR is derived from the left-tail quantile of rescaled returns, and ES is approximated by averaging quantiles below the VaR level. The method delivers robust, distribution-free estimates of extreme losses and captures skewness, heavy tails, and leverage effects. Simulation experiments and empirical analysis show that it often outperforms established models, including GARCH and joint VaR-ES conditional-quantile approaches. An application to daily returns on major international stock indices, spanning the COVID-19 period, highlights its effectiveness in capturing risk dynamics.