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Modelling, Estimating and Validating Multidimensional Distribution Functions With Applications to Ri
Company: University of Kaiserslautern
Year Of Publication: 2003
Month Of Publication: December
Pages: 245
Download Count: 410
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 3-20-2007
Publisher: Administrator
The question of how to model dependence structures between financial assets wasrevolutionized since the last decade when the copula concept was introduced infinancial research. Even though the concept of splitting marginal behavior anddependence structure (described by a copula) of multidimensional distributionsalready goes back to Sklar (1955) and Hoeffding (1940), there were very littleempirical efforts done to check out the potentials of this approach.The aim of this thesis is to figure out the possibilities of copulas for modelling,estimating and validating purposes. Therefore we extend the class ofArchimedean Copulas via a transformation rule to new classes and come up withan explicit suggestion covering the Frank and Gumbel family. We introduce acopula based mapping rule leading to joint independence and as results of thismapping we present an easy method of multidimensional 2 testing and a newestimate for high dimensional parametric distributions functions. Different waysof estimating the tail dependence coefficient, describing the asymptotic probabilityof joint extremes, are compared and improved. The limitations of ellipticaldistributions are carried out and a generalized form of them, preserving theirapplicability, is developed. We state a method to split a (generalized) ellipticaldistribution into its radial and angular part. This leads to a positive definite robustestimate of the dispersion matrix (here only given as a theoretical outlook).The impact of our findings is stated by modelling and testing the return distributionsof stock-, currency-, oil related commodities- and LME metal baskets;showing the crash stability of real estate based firms and the existence of nonlineardependence in between the yield curve.
Junker, Markus Sign in to follow this author
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