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Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified

Author

Listed:
  • Mohamed El Ghourabi
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - 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 - GENES - 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)

  • Fedya Telmoudi

    (LARODEC - Laboratoire de Recherche Opérationnelle de Décision et de Contrôle de Processus - Université de Tunis - ISG de Tunis, 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

A two‐step approach for conditional value at risk estimation is considered. First, a generalized quasi‐maximum likelihood estimator is employed to estimate the volatility parameter, then the empirical quantile of the residuals serves to estimate the theoretical quantile of the innovations. When the instrumental density h of the generalized quasi‐maximum likelihood estimator is not the Gaussian density, both the estimations of the volatility and of the quantile are generally asymptotically biased. However, the two errors counterbalance and lead to a consistent estimator of the value at risk. We obtain the asymptotic behavior of this estimator and show how to choose optimally h .

Suggested Citation

  • Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2015. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Post-Print hal-05417346, HAL.
    • Handle: RePEc:hal:journl:hal-05417346
    DOI: 10.1111/jtsa.12136
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