Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Department of Mathematical Sciences
Committee Member 1
Committee Member 2
Author's abstract: There have been many attempts to find a model that can accurately price options. These models are built on many assumptions, including which probability distribution stock returns follow. In this paper, we test several distributions to see which best fit the log returns of 20 different companies over a period between November 1, 2006 to October 31, 2011. If a "best" distribution is found, a modified Black-Scholes model will be defined by modifying the Weiner process. We use Monte Carlo simulations to generate estimated prices under specified parameters, and compare these prices to those simulated by the model using the Weiner process. It was found the Student-t distribution did a better job at modeling the larger time intervals and the 3-parameter lognormal did a better job at modeling the smaller time intervals. We were not able to make any definite conclusion due to the cost of purchasing historical option data.
Richey, Daniel Lee, "The Distribution of Individual Stock Returns in a Modified Black-scholes Option Pricing Model" (2012). Electronic Theses & Dissertations. 1015.