Compound Lévy random bridges and credit risky asset pricing - Ikpe, Dennis Chinemerem (Department of Mathematics and Applied Mathematics, 2016)
In this thesis, we study random bridges of a certain class of Lévy processes and their applications to credit risky asset pricing. In the first part, we construct the compound random bridges(CLRBs) and analyze some tools and properties that make them suitable models for information processes. We focus on the Markov property, dynamic consistency, measure changes and increment distributions. Thereafter, we consider applications in credit risky asset pricing. We generalize the information based credit risky asset pricing framework to incorporate prematurity default possibilities. Lastly we derive closed-form expressions for default trends and intensities for credit risky bonds with CLRB as the background partial information process. We obtain analytical expressions for specific CLRBs. The second part looks at application of stochastic filtering in the current information based asset pricing framework. First, we formulate credit risky asset pricing in the information-based framework as a filtering problem under incomplete information. We derive the Kalman-Bucy filter in one dimension for bridges of Lévy processes with a given finite variance.