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Looking for efficient QML estimation of conditional value-at-risk at multiple risk levels

Author

Listed:
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris)

  • Jean-Michel Zakoïan

    (LFA - Laboratoire de Finance Assurance - Centre de Recherche en Économie et Statistique (CREST) - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique, EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé)

Abstract

We consider joint estimation of conditional Value-at-Risk (VaR) at several levels, in the framework of general GARCH-type models. The conditional VaR at level $\alpha$ is expressed as the product of the volatility and the opposite of the $\alpha$-quantile of the innovation. A standard method is to estimate the volatility parameter by Gaussian Quasi-Maximum Likelihood (QML) in a first step, and to use the residuals for estimating the innovations quantiles in a second step. We argue that the Gaussian QML may be inefficient with respect to more general QML and can even be in failure for heavy tailed conditional distributions. We therefore study, for a vector of risk levels, a two-step procedure based on a generalized QML. For a portfolio of VaR's at different levels, confidence intervals accounting for both market and estimation risks are deduced. An empirical study based on stock indices illustrates the theoretical results.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2016. "Looking for efficient QML estimation of conditional value-at-risk at multiple risk levels," Post-Print hal-05430924, HAL.
    • Handle: RePEc:hal:journl:hal-05430924
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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