Estimation of Expected Shortfall Using Quantile Regression: A Comparison Study

Eliana Christou () and Michael Grabchak ()
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Eliana Christou: University of North Carolina at Charlotte
Michael Grabchak: University of North Carolina at Charlotte

Computational Economics, 2022, vol. 60, issue 2, No 12, 725-753

Abstract: Abstract Expected Shortfall ( $$\mathrm {ES}$$ ES ) is one of the most heavily used measures of financial risk. It is defined as a scaled integral of the quantile of the profit-and-loss distribution up to a certainly confidence level. As such, quantile regression (QR) and the closely related expectile regression (ER) methods are natural techniques for estimating $$\mathrm {ES}$$ ES . In this paper, we survey QR and ER based estimators of ES and introduce several novel variants. We compare the performance of these methods through simulation and through a data analysis based on four major US market indices: the S&P 500 Index, the Russell 2000 Index, the Dow Jones Industrial Average, and the NASDAQ Composite Index. Our results suggest that QR and ER methods often work better than other, more standard, approaches.

Keywords: Expected shortfall; Expectile regression; Quantile regression; Single index; Value-at-risk (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10614-021-10164-z

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