Stochastic Evolution Equations in Portfolio Credit Modelling

We consider a structural credit model for a large portfolio of credit risky assets. By considering the large portfolio limit we introduce a stochastic partial differential equation which describes the evolution of the density of asset values. 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. We also use it to price dynamic credit products such as forward starting CDO tranches.