We consider a structural credit model for a large portfolio of credit riskyassets where the correlation is due to a market factor. By considering thelarge portfolio limit of this system we show the existence of a density processfor the asset values. This density evolves according to a stochastic partialdifferential equation and we establish existence and uniqueness for thesolution taking values in a suitable function space. The loss function of theportfolio is then a function of the evolution of this density at the defaultboundary. We develop numerical methods for pricing and calibration of the modelto credit indices and consider its performance pre and post credit crunch.Finally, we give further examples illustrating the valuation of exotic creditproducts, specifically forward starting CDOs.
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