Physical Sciences and Mathematics Commons^™

A Conditioned Gaussian-Poisson Model For Default Phenomena, Tyler Brannan

LSU Doctoral Dissertations

We introduce a new model to study the behavior of a portfolio of defaultable assets. We refer to this model as the Gaussian-Poisson model. It builds upon one-factor Gaussian copula models and Poisson models (specifically Cox processes). Our model utilizes a random variable Y along with probability measures ℙ^• and ℙ^†. The measures ℙ^• and ℙ^† will act as market pricing measures and are obtained via conditioning. The random variable Y will act as a default descriptor.

We provide the distribution of Y under both ℙ^• and ℙ^†. We use a conditional …

Stochastic And Copula Models For Credit Derivatives, Chao Meng

LSU Doctoral Dissertations

We prove results relating to the exit time of a stochastic process from a region in N-dimensional space. We compute certain stochastic integrals involving the exit time. Taking a Gaussian copula model for the hitting time behavior, we prove several results on the sensitivity of quantities connected with the hitting times to parameters of the model, as well as the large-N behavior. We discuss the relationship of these results to certain credit derivative instruments. Relevant simulations are presented.