A Poisson Model with Common Shocks for CDO Valuation

Abstract

A collateralized debt obligation is a credit risk product created in tranches from a portfolio of debt instruments. To value tranches, it is critical to model multiple default correlations in order to derive the appropriate loss function. Conditional independence is the usual assumption in this regard, but it ignores meaningful correlated shocks. Models assuming conditional dependence are improvements except that the number of parameters makes model calibration very challenging. A Poisson model with common shocks for derivation of the CDO loss function assumes conditional dependence and reduces the number of model parameters by grouping firms with equal credit ratings. Implementation becomes more efficient, and such a model can correct the tranche mispricing produced by the assumption of conditional independence.