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@article{ Scherer2009, title = {Correlation Smile Matching for CDO Tranches with α Stable Distributions and Fitted Archimedan Copulas}, author = {Scherer, Wolfgang and Prange, Dirk}, journal = {Quantitative Finance}, number = {4}, pages = {439-449}, volume = {9}, year = {2009}, doi = {https://doi.org/10.1080/14697680802464428}, urn = {https://nbn-resolving.org/urn:nbn:de:0168-ssoar-221341}, 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.}, }