Date of Award

January 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Frederi Viens

Committee Member 1

Jose Figueroa-Lopez

Committee Member 2

Michael Levine

Committee Member 3

Jonathon Peterson


We constructed a white noise theory for the Canonical Levy process by Sole, Utzet, and Vives. The construction is based on the alternative construction of the chaos expansion of square integrable random variable. Then, we showed a Clark-Ocone theorem in L^2(P) and under the change of measure. The result from the Clark-Ocone theorem was used for the mean-variance hedging problem and applied it to stochastic volatility models such as the Barndorff-Nielsen and Shepard model model and the Bates model. A Donsker Delta approach is employed on a Binary option to solve the mean-variance hedging problem. Finally, we are able to derive the Delta and Gamma for a barrier and lookback options for an exp-Levy process using the methodology of Bernis, Gobet, and Kohatsu-Higa by employing a dominating process.