Stable Mixture GARCH Models
38 Pages Posted: 23 Sep 2011 Last revised: 11 Jun 2020
Date Written: October 18, 2011
Abstract
A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. An improved method (in terms of speed and accuracy) is developed for the computation of the stable Paretian density. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. The model is straightforwardly extended to the multivariate setting by using an independent component analysis framework. The tractability of the relevant characteristic function then facilitates portfolio optimization using expected shortfall as the downside risk measure.
Keywords: Density Forecasting, Expected Shortfall, Fat Tails, ICA, GARCH, Mixtures, Portfolio Selection, Stable Paretian Distribution, Value-at-Risk
JEL Classification: C13, C16, C22, C32, G17
Suggested Citation: Suggested Citation
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