Doctor of Philosophy (PhD)
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 probability to examine expected portfolio and tranche losses, with applications including credit default swaps and collateralized debt obligations. The Gaussian-Poisson model requires a choice of an intensity model. We examine a portfolio loss' dependence upon parameters of the intensity model. Finally, we present three possible models of the intensity process.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Brannan, Tyler, "A Conditioned Gaussian-Poisson Model for Default Phenomena" (2016). LSU Doctoral Dissertations. 3532.