Empirical Estimation of Tail Dependence Using Copulas. Application to Asian Markets

Cyril Caillault (1) , Dominique Guegan (1)

1 IDHE - Institutions et Dynamiques Historiques de l'Economie

This paper introduces non-parametric estimators for upper and lower tail dependence whose confidence intervals are obtained with a bootstrap method. We call these estimators "Naïve estimators" as they represent a discretization of Joe's formulae (1997)\nocite{Joe} linking copulas to tail dependence. We apply the methodology to an empirical data set composed of three composite indexes for the three Tigers (Thailand, Malaysia and Indonesia). The extremes show a dependence structure which is symmetric for the Thai and Malaysian markets and asymmetric for the Thai and Indonesian markets and for the Malaysian and the Indonesian markets. Using these results we estimate the copula (which belongs to the Student or Archimedean copula families) for each pair of markets by two methods. Finally, we provide risk measurements using the best copula associated to each pair of markets.

Mots clés: Tail dependence; Non-parametric Estimation; Semi-parametric estimation; Bootstrap; Risk's measure.; Risk's measure

Domaines: Economies et finances; Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Cyril Caillault, Dominique Guegan. Empirical Estimation of Tail Dependence Using Copulas. Application to Asian Markets. Quantitative Finance, 2005, 5, pp.489 - 501. ⟨halshs-00180865⟩