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Journal of Financial Econometrics Advance Access originally published online on February 9, 2008
Journal of Financial Econometrics 2008 6(2):231-252; doi:10.1093/jjfinec/nbn001
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

Estimating Value at Risk and Expected Shortfall Using Expectiles

James W. Taylor
     Saïd Business School, University of Oxford

Address for correspondence: Saïd Business School, University of Oxford, Park End Street, Oxford OX1 1HP, UK. Tel.: +44 (0)1865 288927; Fax: +44 (0)1865 288805; email: james.taylor{at}sbs.ox.ac.uk

JEL Classification: C22, C53, C10


   Abstract

Expectile models are derived using asymmetric least squares. A simple formula has been presented that relates the expectile to the expectation of exceedances beyond the expectile. We use this as the basis for estimating the expected shortfall. It has been proposed that the {theta} quantile be estimated by the expectile for which the proportion of observations below the expectile is {theta}. In this way, an expectile can be used to estimate value at risk. Using expectiles has the appeal of avoiding distributional assumptions. For univariate modeling, we introduce conditional autoregressive expectiles (CARE). Empirical results for the new approach are competitive with established benchmarks methods.

KEYWORDS: financial risk, asymmetric least squares, expectiles, conditional autoregressive expectiles


I am grateful for the helpful comments of Jan de Gooijer and Keming Yu. I am also grateful for the insightful comments of an associate editor and two referees.


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J. W. Taylor
Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall
J. Financial Econometrics, July 1, 2008; 6(3): 382 - 406.
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