Correlation Smile Matching with Alpha-Stable Distributions and Fitted Archimedan Copula Models
by Dirk Prange of DrKW, and Wolfgang Scherer of DrKW
March 14, 2006
Abstract: As an extension of the standard Gaussian copula model we present a generalization 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 to others which provide fatter tails. 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 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. Market premia, even through the correlation crisis, 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.
