## Modeling Dependence in Financial Data with Semiparametric Archimedean Copulas

published: Aug. 21, 2009,   recorded: July 2009,   views: 858
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# Slides

0:00 Slides Modeling Dependence in Financial Data with Semiparametric Archimedean Copulas Outline (1) Outline (2) Copulas and Computational Finance Definition of a copula function Eliminating the marginals Eliminating the marginals (continued) Some bivariate copula functions Some bivariate copula densities Parametric, non-parametric and semiparametric copulas Outline (3) Bivariate Archimedean copulas Parameterizations of Bivariate Archimedean copulas Some plots of g for parametric Archimedean copulas periments with financial data Modeling g Estimation of g Outline (4) The data Modeling the marginal distributions Benchmark copula estimation methods Experimental protocol Average log-likelihood for each method on each problem Some copula density estimates Summary Thanks! - Questions

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# Description

Copulas are useful tools for the construction of multivariate models because they allow to link univariate marginals into a joint model with arbitrary dependence structure. While non-parametric copula models can have poor generalization performance, standard parametric copulas often lack expressive capacity to capture the dependencies present in financial data. In this work, we propose a novel semiparametric bivariate Archimedean copula model that is expressed in terms of a latent function. This latent function is approximated using a basis of natural splines and the model parameters are selected by maximum penalized likelihood. Experiments on financial data are used to evaluate the accuracy of the proposed estimator with respect to other benchmark methods: Two flexible estimators of Archimedean copulas previously introduced in the literature, two approaches for copula estimation that allow for more general dependencies and three parametric copulas models. The proposed semiparametric copula model has excellent in and out-of-sample performance, which makes it a useful tool for modeling multivariate financial data.