Date of Award
January 2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Statistics
First Advisor
Frederi Viens
Committee Member 1
Jose Figueroa-Lopez
Committee Member 2
Michael Levine
Committee Member 3
Jonathon Peterson
Abstract
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.
Recommended Citation
Navarro, Rolando Dangnanan, "Malliavin Calculus in the Canonical Levy Process: White Noise Theory and Financial Applications." (2015). Open Access Dissertations. 1422.
https://docs.lib.purdue.edu/open_access_dissertations/1422