Empirical estimation of tail dependence using copulas: application to Asian markets

Abstract

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 'naive estimators' as they represent a discretization of Joe's formulae 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 with each pair of markets.

Modeling International Financial Returns with a Multivariate Regime Switching Copula

“…These confidence intervals are obtained from 500 bootstrap replications of the data. We use the bootstrap method proposed by Caillault & Guégan (2005) for the selection of the best threshold to estimate tail dependence. We are not using it to select an optimal threshold but simply to have an idea of the variability of the estimated quantile dependence.…”

Copula Estimation

“…Lee and Long [34] consider extensions and empirical applications of multivariate GARCH models with copula-based specifications of dependence among the vectors components. Among other results, Caillault and Guégan [4] provide nonparametric estimates of tail dependence parameters for Asian financial indices. Smith [44,45] discusses applications of copulas in sample selection and regime switching models.…”

A multivariate Lévy process model with linear correlation

“…The limiting values lim u↓0 λ LL (u) and lim u↓0 λ UU (u) are often called, respectively, the lower and the upper tail-dependence coefficients, and their estimation methods and applications to financial markets have been intensively studied. For details, see, for example, Caillault and Guégan [5], Frahm et al [10], Malevergne and Sornette [18], and Poon et al [21]. Remark 4.2.…”