  We consider a structural credit model for a large portfolio of credit risky
assets where the correlation is due to a market factor. By considering the
large portfolio limit of this system we show the existence of a density process
for the asset values. This density evolves according to a stochastic partial
differential equation and we establish existence and uniqueness for the
solution taking values in a suitable function space. The loss function of the
portfolio is then a function of the evolution of this density at the default
boundary. We develop numerical methods for pricing and calibration of the model
to credit indices and consider its performance pre and post credit crunch.
Finally, we give further examples illustrating the valuation of exotic credit
products, specifically forward starting CDOs.
