Graphical Models for Correlated Defaults

by I. Onur Filiz of the University of California, Berkeley,
Xin Guo of the University of California, Berkeley,
Jason Morton of the University of California, Berkeley, and
Bernd Sturmfels of the University of California, Berkeley

September 21, 2008

Abstract: A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These techniques also provide a calibration algorithm based on maximum likelihood estimation. Finally, the model is compared with standard normal copula model in terms of tails of the loss distribution and implied correlation smile.

JEL Classification: C51, G33.

Keywords: graphical models, default correlation, correlation smile, dynamic models, normal copula.

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