The Distribution of Individual Stock Returns in a Modified Black-scholes Option Pricing Model

<p> 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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2012

Author dc:creator

• Richey, Daniel Lee

Contributors dc:contributor

• Jonathan Duggins
• John Barkoulas

• ETD
• Black-Scholes
• Weiner process
• Mathematical finance
• Finance and Financial Management
• Mathematics
• Other Mathematics
• Physical Sciences and Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1015

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2048