Dear Jalaltarin:I've written this before but I think that it can be useful for you.Which Archimedean Copula is the right one?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.Tools for sampling Multivariate Archimedean CopulasA hurdle for practical implementation of any multivariate Archimedean copula was the absence of an efficient method for generating them. The most frequently used approach named conditional distribution one, involves differentiation step for each dimension of the problem. For this reason, it is not feasible in higher dimension. Marshall and Olkin proposed an alternative method, which is computationally more straightforward than the conditional distribution approach. We present the tools necessary for understand it and use it. We introduce the Laplace Transform and its role in the generation of multivariate Archimedean copulas. In order to cover the gap between the theory and its practical implementation VBA code and R one are provided.The codes sheets are available from the author on request.I hope this helps. Mario R.
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