  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.

Computational Finance;Probability;Risk Management;Statistical Finance