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

31 Pages Posted: 22 Dec 2015

See all articles by Mohamed El Ghourabi

Mohamed El Ghourabi

University of Tunis, Larodec

Christian Francq

University of Lille III

Fedya Telmoudi

University of Tunis

Date Written: January 2016

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.

Keywords: APARCH, conditional VaR, distortion risk measures, GARCH, generalized quasi‐maximum likelihood estimation, instrumental density

Suggested Citation

El Ghourabi, Mohamed and Francq, Christian and Telmoudi, Fedya, Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified (January 2016). Journal of Time Series Analysis, Vol. 37, Issue 1, pp. 46-76, 2016, Available at SSRN: https://ssrn.com/abstract=2706916 or http://dx.doi.org/10.1111/jtsa.12136

Mohamed El Ghourabi (Contact Author)

University of Tunis, Larodec ( email )

Christian Francq

University of Lille III ( email )

Domaine du Pont de bois
Villeneuve D'Ascq Cedex, 59653
France

Fedya Telmoudi

University of Tunis ( email )

92, Rue 9 Avril
Tunis, 1938 -1007
Tunisia

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