GARCH-UGH: A bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series

TL;DR

This paper introduces GARCH-UGH, a new bias-reduction method for more accurately estimating dynamic extreme Value-at-Risk in financial time series, improving risk management practices.

Contribution

The paper proposes a novel two-step bias-reduced estimation approach combining AR-GARCH filtering with extreme quantile estimation for dynamic VaR.

Findings

GARCH-UGH outperforms traditional methods in accuracy.

Improved in-sample and out-of-sample backtesting results.

Applicable to various financial time series.

Abstract

The Value-at-Risk (VaR) is a widely used instrument in financial risk management. The question of estimating the VaR of loss return distributions at extreme levels is an important question in financial applications, both from operational and regulatory perspectives; in particular, the dynamic estimation of extreme VaR given the recent past has received substantial attention. We propose here a two-step bias-reduced estimation methodology called GARCH-UGH (Unbiased Gomes-de Haan), whereby financial returns are first filtered using an AR-GARCH model, and then a bias-reduced estimator of extreme quantiles is applied to the standardized residuals to estimate one-step ahead dynamic extreme VaR. Our results indicate that the GARCH-UGH estimates are more accurate than those obtained by combining conventional AR-GARCH filtering and extreme value estimates from the perspective of in-sample and out-of-sample backtestings of historical daily returns on several financial time series.