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

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  • Hibiki Kaibuchi
  • Yoshinori Kawasaki
  • Gilles Stupfler

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.

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  • Hibiki Kaibuchi & Yoshinori Kawasaki & Gilles Stupfler, 2021. "GARCH-UGH: A bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Papers 2104.09879, arXiv.org.
    • Handle: RePEc:arx:papers:2104.09879
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    2. Marta Małecka & Radosław Pietrzyk, 2024. "A spectral approach to evaluating VaR forecasts: stock market evidence from the subprime mortgage crisis, through COVID-19, to the Russo–Ukrainian war," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4533-4567, October.

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