In financial markets under uncertainty, the classical Black-Scholes model cannot explain the empirical facts such as fat tails observed in the probability density. To overcome this drawback, during the last decade, Lévy process and stochastic volatility models were introduced to financial modeling. Today crude oil futures markets are highly volatile. It is the purpose of this dissertation to develop a mathematical framework in which American options on crude oil futures contracts are priced more effectively than by current methods. In this work, we use the Variance Gamma process to model the futures price process. To generate the underlying process, we use a random tress method so that we evaluate the option prices at each tree node. Through fifty replications of a random tree, the averaged value is taken as a true option price. Pricing performance using this method is accessed using American options on crude oil commodity contracts from December 2003 to November 2004. In comparison with the Variance Gamma model, we price using the Black-Scholes model as well. Over the entire sample period, a positive skewness and high kurtosis, especially in the short-term options, are observed. In terms of pricing errors, the Variance Gamma process performs better than the Black-Scholes model for the American options on crude oil commodities. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of
the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2008. / Date of Defense: July 10, 2008. / Variance Gamma Process, American Options on Crude Oil Futures Commodity Calibration, Random Tree Method, Lévy Process / Includes bibliographical references. / Craig A. Nolder, Professor Directing Dissertation; Fred Huffer, Outside Committee Member; Bettye Anne Case, Committee Member; Alec N. Kercheval, Committee Member; Jack Quine, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_168852 |
| Contributors | Yoo, Eunjoo (authoraut), Nolder, Craig A. (professor directing dissertation), Huffer, Fred (outside committee member), Case, Bettye Anne (committee member), Kercheval, Alec N. (committee member), Quine, Jack (committee member), Department of Mathematics (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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