Modelling and Estimation for Bivariate Financial Returns

Thomas Fung and Eugene Seneta

International Statistical Review, 2010, vol. 78, issue 1, 117-133

Abstract: Maximum likelihood estimates are obtained for long data sets of bivariate financial returns using mixing representation of the bivariate (skew) Variance Gamma (VG) and two (skew) t distributions. By analysing simulated and real data, issues such as asymptotic lower tail dependence and competitiveness of the three models are illustrated. A brief review of the properties of the models is included. The present paper is a companion to papers in this journal by Demarta & McNeil and Finlay & Seneta. Des estimateurs maximum de vraisemblance sont obtenus pour de longues séries bivariées de rendements financiers modélisées à partir d'un mélange (asymétrique) de type Variance‐Gamma et de deux mélanges (asymétriques) de type Student. L'analyse de données simulées et réelles permet d'illustrer quelques‐uns des aspects asymptotiques de ces trois modèles, tels que les dépendances asymptotiques des extrêmes dans la queue gauche, et leurs performances. Un bref compte‐rendu des propriétés de ces modèles est également inclus. Le présent travail accompagne et complète les articles de Demarta et McNeil (2005) et de Finlay et Seneta (2008) parus dans la même revue.

Date: 2010
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