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Correlation Smile Matching for CDO Tranches with α Stable Distributions and Fitted Archimedan Copulas

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Scherer, Wolfgang; Prange, Dirk

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Abstract As an extension of the standard Gaussian copula model to price CDO tranche swaps we present a generalization of a one-factor copula model based on stable distributions. For special parameter values these distributions coincide with Gaussian or Cauchy distributions, but changing the parameters allows a continuous deformation away from the Gaussian copula. All these factor copulas are embedded into a framework of stochastic correlations. We furthermore generalize the linear dependency in the usual factor approach to a more general Archimedean copula dependency between the individual trigger variable and the common latent factor. Our analysis is carried out on a non-homogeneous correlation structure of the underlying portfolio. CDO tranche market premia, even through the correlation crisis in May 2005, can be reproduced by certain models. From a numerical perspective all these models are simple since calculations can be reduced to one dimensional numerical integrals.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method theory application
Free Keywords Copulas; Correlation modelling; Credit derivatives; Credit models
Document language English
Publication Year 2009
Page/Pages p. 439-449
Journal Quantitative Finance, 9 (2009) 4
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)