Singular perturbation methods in credit derivative modeling

This thesis introduces the dynamical pricing model and approximation method in pricing a "Collateralized Debt Obligation"(CDO). For this purpose we use a two-dimensional, self-affecting Markov process of discrete-valued aggregate loss process and stochastic factor process in its intensity. We review several models for pricing of multiname credit derivative products and explain in detail a two-dimensional Markov intensity model proposed by Halperin and Arnsdorf.;Using the model by Halperin and Arnsdorf, we derive the Kolmogorov forward partial differential equation for the transition density function of the underlying two-dimensional Markov process. We use the singular perturbation method to obtain an approximate solution to this partial differential equation in the case of a fast mean reverting stochastic intensity model. We perform an error analysis to determine the accuracy of our approximate solution.