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Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations

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In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series: volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects

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  • Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2008. "Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations," Documents de travail du Centre d'Economie de la Sorbonne b08027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b08027
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    4. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.

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    Keywords

    BL-GARCH process; elliptical distribution; leverage effects; maximum likelihood; Monte Carlo method; volatility clustering;
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