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Which Archimedean Copula is the Right One?

by Mario R. Melchiori of the Universidad Nacional del Litoral

September 2003

Abstract: This paper presents the concept of copula from a practical standpoint. Given the widened use of the multinormal distribution, we argue its inadequacy, while advocate for using the copula as an alternative and better approach. We examine what the copulas are used for within of risk management. Then we expose a guide to choose both the margins and the Archimedean copula that better fit to data. In addition, we provide an algorithm to simulate random bivariate from Archimedean copula. In order to cover the gap between the theory and its practical implementation VBA codes are provided. They are used in a numerical example that illustrates the use of the copula in the pricing of a first-at-default contract. Two spreadsheets accompany to paper, by presenting step by step all practical applications covered.

Keywords: Copula, Kendall Tau, Dependence, and Credit Derivatives.

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Related reading: Sampling from Archimedean Copulas