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This thesis examines the dependence structures between commodity futures and corresponding commodity producer equity indices in bearish, bullish and normal market conditions. We study commodity futures and producer indices in the energy, precious metals, gold and agriculture commodity markets using daily return data that ranges from 16 December 2005 to 28 June 2019. We employ the cross-quantilogram approach developed by Han et al. (2016) to examine dependence structures in the full quantile range, which represents different market states. Furthermore, we control for different lag structures, uncertainties and time-varying dependence structures. From our results we conclude the following: 1) There are time-varying asymmetric and symmetric dependencies in different commodity markets. There is asymmetric dependence between commodity futures and producer indices in the precious metals, gold and agricultural markets. In the oil market, the relationship is symmetrical. No relationship is found in the natural gas market. 2) Heterogenous dependence structures are identified in the gold, precious metals and agricultural commodity markets. The oil market uncovers homogenous dependence structures. 3) The observed spillover in all markets occur in the very short run, at one day, and dissipates after a week and additionally after a month. Our results provide new information regarding commodity diversification attributes which can be useful to investors. Our results also provide important policy implications: Since volatility spillovers between commodity futures and producer indices may deter investors from including commodities in their portfolios, as they might lose their diversifier qualities, it is important to enforce policies that will prevent the spillovers between the assets. Further, regulations of the commodity futures markets could be an alternative to reduce the spillovers.

Cette thèse a pour but le développement de certains aspects de la modélisation de la dépendance dans la gestion des risques en dimension plus grande que un. Le premier chapitre est constitué d'une introduction générale. Le deuxième chapitre est constitué d'un article s'intitulant « Estimating Bivariate Tail : a copula based approach », soumis pour publication. Il concerne la construction d'un estimateur de la queue d'une distribution bivariée. La construction de cet estimateur se fonde sur une méthode de dépassement de seuil (Peaks Over Threshold method) et donc sur une version bivariée du Théorème de Pickands-Balkema-de Haan. La modélisation de la dépendance est obtenue via la Upper Tail Dependence Copula. Nous démontrons des propriétés de convergence pour l'estimateur ainsi construit. Le troisième chapitre repose sur un article: « A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation», soumis pour publication. Nous abordons le problème de l'extension de mesures de risque classiques, comme la Value-at-Risk et la Conditional-Tail-Expectation, dans un cadre multidimensionnel en utilisant la fonction de Kendall multivariée. Enfin, dans le quatrième chapitre de la thèse, nous proposons un estimateur des courbes de niveau d'une fonction de répartition bivariée avec une méthode plug-in. Nous démontrons des propriétés de convergence pour les estimateurs ainsi construits. Ce chapitre de la thèse est lui aussi constitué d'un article, s'intitulant « Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory», accepté pour publication dans la revue ESAIM:Probability and Statistics. / In this PhD thesis we consider different aspects of dependence modeling with applications in multivariate risk theory. The first chapter is constituted by a general introduction. The second chapter is essentially constituted by the article “Estimating Bivariate Tail: a copula based approach”, actually submitted for publication. It deals with the problem of estimating the tail of a bivariate distribution function. We develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. The dependence structure between the marginals in the upper tails is described by the Upper Tail Dependence Copula. Then we construct a two-dimensional tail estimator and study its asymptotic properties. The third chapter of this thesis is based on the article “A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation” and submitted for publication. We propose a multivariate generalization of risk measures as Value-at-Risk and Conditional-Tail-Expectation and we analyze the behavior of these measures in terms of classical properties of risk measures. We study the behavior of these measures with respect to different risk scenarios and stochastic ordering of marginals risks. Finally in the fourth chapter we introduce a consistent procedure to estimate level sets of an unknown bivariate distribution function, using a plug-in approach in a non-compact setting. Also this chapter is constituted by the article “Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory”, accepted for publication in ESAIM: Probability and Statistics journal.