Correlation-dependent Credit Structural Model
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 for credit spreads implied by the model and
explore how the model price 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 two 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 Valuation of Correlation-dependent Credit Derivatives Using a
Structural Model
John Hull, Mirela Predescu, and Alan White