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Statistical estimation errors of VaR under ARCH returns

par Taniai, Hiroyuki ;Taniguchi, Masanobu
Référence Journal of statistical planning and inference, 138, 11, page (3568-3577)
Publication Publié, 2008-11

Article révisé par les pairs

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Résumé :

In this paper we discuss some problems of existing methods for calculating the Value-at-Risk (VaR) in ARCH setting. It should be noted that the commonly used approaches often confuse the true innovations with the empirical residuals, i.e., estimation errors for unknown ARCH parameters are ignored. We adjust this by using the asymptotics of the residual empirical process, and propose a feasible VaR which, according to the spirit of VaR, keeps the assets away from a specified risk with high confidence level. Its meaningfulness in comparison with the usual VaR will be illustrated clearly by numerical studies. © 2008 Elsevier B.V. All rights reserved.