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Journal of Financial Econometrics Advance Access published online on May 16, 2008
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbn007
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org

Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall

James W. Taylor
     Saïd Business School, University of Oxford

Address correspondence to James W. Taylor, Saïd Business School, University of Oxford, Park End Street, Oxford OX1 1HP, UK, or e-mail: james.taylor{at}sbs.ox.ac.uk.

JEL Classification: C22, C53, G10


  Abstract

We propose exponentially weighted quantile regression (EWQR) for estimating time-varying quantiles. The EWQR cost function can be used as the basis for estimating the time-varying expected shortfall associated with the EWQR quantile forecast. We express EWQR in a kernel estimation framework, and then modify it by adapting a previously proposed double kernel estimator in order to provide greater accuracy for tail quantiles that are changing relatively quickly over time. We introduce double kernel quantile regression, which extends the double kernel idea to the modeling of quantiles in terms of regressors. In our empirical study of 10 stock returns series, the versions of the new methods that do not accommodate the leverage effect were able to outperform GARCH-based methods and CAViaR models.

KEYWORDS: exponential weighting, financial risk, kernel smoothing, kernel density estimation, quantile regression

We acknowledge the helpful comments of Jan De Gooijer, Ev Gardner, Patrick McSharry, and Keming Yu on an earlier version of this paper. We are also grateful for the useful comments of the editor, Eric Renault, and two referees.

Received November 2, 2006; revised November 9, 2007; accepted April 11, 2008


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