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ESTIMATION-ADJUSTED VAR

Published online by Cambridge University Press:  08 January 2013

Christian Gourieroux  and
Jean-Michel Zakoïan
Christian Gourieroux
Affiliation:
CREST and University of Toronto
Jean-Michel Zakoïan*
Affiliation:
CREST and University Lille 3 (EQUIPPE)
*
*Address correspondence to Jean-Michel Zakoan, CREST, 15 Boulevard G. Péri, 92245 Malakoff Cedex, France; e-mail: zakoian@ensae.fr.
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Abstract

Standard risk measures, such as the value-at-risk (VaR), or the expected shortfall, have to be estimated, and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the profit and loss variable induces an asymptotic bias of order 1/n in the coverage probabilities. This paper shows how to correct for this bias by introducing a new estimator of the VaR, called estimation-adjusted VaR (EVaR). This adjustment allows for a joint treatment of theoretical and estimation risks, taking into account their possible dependence. The estimator is derived for a general parametric dynamic model and is particularized to stochastic drift and volatility models. The finite sample properties of the EVaR estimator are studied by simulation and an empirical study of the S&P index is proposed.

Type
Research Articles
Information
Econometric Theory , Volume 29 , Issue 4 , August 2013 , pp. 735 - 770
Copyright
Copyright © Cambridge University Press 2012 

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