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Multi-level Conditional VaR Estimation in Dynamic Models

Author

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  • Christian Francq

    (CREST)

  • Jean-Michel Zakoian

    (CREST)

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

Suggested Citation

  • Christian Francq & Jean-Michel Zakoian, 2014. "Multi-level Conditional VaR Estimation in Dynamic Models," Working Papers 2014-01, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2014-01
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    References listed on IDEAS

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    Cited by:

    1. 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.

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    More about this item

    Keywords

    GARCH; Distortion Risk Measures; Quasi-Maximum Likelihood; Value-at-Risk;
    All these keywords.

    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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