Stable Mixture GARCH Models

38 Pages Posted: 23 Sep 2011 Last revised: 11 Jun 2020

See all articles by Simon A. Broda

Simon A. Broda

University of Zurich - Department of Banking and Finance

Markus Haas

University of Kiel - Faculty of Economics and Social Sciences

Jochen Krause

University of Zurich - Department of Banking and Finance

Marc S. Paolella

University of Zurich - Department of Banking and Finance; Swiss Finance Institute

Sven C. Steude

University of Zurich - Department of Banking and Finance

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

Broda, Simon A. and Haas, Markus and Krause, Jochen and Paolella, Marc S. and Steude, Sven Christian, Stable Mixture GARCH Models (October 18, 2011). Swiss Finance Institute Research Paper No. 11-39, Journal of Econometrics, Vol. 172, No. 2, 2013, Available at SSRN: https://ssrn.com/abstract=1932287 or http://dx.doi.org/10.2139/ssrn.1932287

Simon A. Broda

University of Zurich - Department of Banking and Finance ( email )

Plattenstr 32
Zurich, 8032
Switzerland

Markus Haas

University of Kiel - Faculty of Economics and Social Sciences ( email )

Kiel
Germany

Jochen Krause

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland
+41446342814 (Phone)

HOME PAGE: http://www.bf.uzh.ch

Marc S. Paolella (Contact Author)

University of Zurich - Department of Banking and Finance

Plattenstr. 14
Zürich, 8032
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Sven Christian Steude

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 32
Zürich, CH-8032
Switzerland

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