Malliavin Calculus in the Canonical Levy Process: White Noise Theory and Financial Applications.

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Year

2015

Author dc:creator

• Navarro, Rolando Dangnanan

Contributors dc:contributor

• Frederi Viens
• Jose Figueroa-Lopez
• Michael Levine
• Jonathon Peterson

• Clark-Ocone theorem
• exotic options
• Levy processes
• Malliavin calculus
• mean-variance hedging
• white noise analysis

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/1422

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-2638