Bayesian Inference on GARCH Models Using the Gibbs Sampler

Posted: 6 Apr 1999

See all articles by Luc Bauwens

Luc Bauwens

Université catholique de Louvain

Michel Lubrano

Ecole des Hautes Etudes en Sciences Sociales (EHESS)

Abstract

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analyti-cal knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied to each coordinate of the poste-rior density. The full conditional densities are evaluated and inverted numerically to obtain random draws of the joint posterior. The method is shown to be feasible and competitive compared with importance sampling and the Metropolis-Hastings algorithm. It is applied to estimate an asymmetric Student-GARCH model for the return on a stock exchange index, and to compute predictive option prices on the index. We prove, moreover, that a flat prior on the degrees of freedom parameter leads to an improper posterior density.

Keywords: Bayesian inference, GARCH, Gibbs sampler, Monte Carlo, Option pricing.

JEL Classification: C11, C15, C22, C32

Suggested Citation

Bauwens, Luc and Lubrano, Michel, Bayesian Inference on GARCH Models Using the Gibbs Sampler. Available at SSRN: https://ssrn.com/abstract=156707

Luc Bauwens (Contact Author)

Université catholique de Louvain ( email )

CORE
34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium
32 10 474321 (Phone)
32 10 474301 (Fax)

Michel Lubrano

Ecole des Hautes Etudes en Sciences Sociales (EHESS) ( email )

Greqam, Vieille Charité
2 rue de la Charité
13002 Marseille
France

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