On heavy-tailed risks under Gaussian copula: The effects of marginal transformation

Bikramjit Das and Vicky Fasen-Hartmann

Journal of Multivariate Analysis, 2024, vol. 202, issue C

Abstract: In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets varies depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so-called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.

Keywords: Asymptotic tail independence; Gaussian copula; Heavy tails; Multivariate regular variation; Tail risk (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.jmva.2024.105310

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