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ABSTRACT
In 1976 Black and Cox proposed a structural model where an obligor defaults when the value of its assets
hits a certain barrier. In 2001 Zhou showed how the model can be extended to two obligors whose assets
are correlated. In this paper we show how the model can be extended to a large number of different
obligors. The correlations between the assets of the obligors are determined by one or more factors. We
examine the dynamics of credit spreads implied by the model and explore how the model prices tranches
of collateralized debt obligations (CDOs). We compare the model with the widely used Gaussian copula
model of survival time and test how well the model fits market data on the prices of CDO tranches. We
consider three extensions of the model. The first reflects empirical research showing that default
correlations are positively dependent on default rates. The second reflects empirical research showing that
recovery rates are negatively dependent on default rates. The third reflects research showing that market
prices are consistent with heavy tails for both the common factor and the idiosyncratic factor in a copula
model.
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