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Multi-level Conditional VaR Estimation in Dynamic Models

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 conditional heteroskedastic models. The volatility is estimated by Quasi-Maximum Likelihood (QML) in a first step, and the residuals are used to estimate the innovations quantiles in a second step. The joint limiting distribution of the volatility parameter and a vector of residual quantiles is derived. We deduce confidence intervals for general Distortion Risk Measures (DRM) which can be approximated by a finite number of VaR’s. We also propose an alternative approach based on non Gaussian QML which, although numerically more cumbersome, has interest when the innovations distribution is fat tailed. An empirical study based on stock indices illustrates the theoretical findings
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2014. "Multi-level Conditional VaR Estimation in Dynamic Models," Post-Print hal-05430959, HAL.
    • Handle: RePEc:hal:journl:hal-05430959
    DOI: 10.1007/978-3-319-03395-2_1
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    2. Francq, Christian & Zakoian, Jean-Michel, 2015. "Looking for efficient qml estimation of conditional value-at-risk at multiple risk levels," MPRA Paper 67195, University Library of Munich, Germany.

    More about this item

    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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