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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Richey, Daniel Lee"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Jonathan Duggins","John Barkoulas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:41Z","subjects":["ETD","Black-Scholes","Weiner process","Mathematical finance","Finance and Financial Management","Mathematics","Other Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1015","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jonathan Duggins","John Barkoulas"]},{"key":"dc:creator","label":"Author","values":["Richey, Daniel Lee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-02-25T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Black-Scholes","Weiner process","Mathematical finance","Finance and Financial Management","Mathematics","Other Mathematics","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1015"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["The Distribution of Individual Stock Returns in a Modified Black-scholes Option Pricing Model"]}]}],"canonical_facts":{"dc:contributor":["Jonathan Duggins","John Barkoulas"],"dc:creator":["Richey, Daniel Lee"],"dc:date.available":["2014-02-25T08:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1015"],"dc:subject":["ETD","Black-Scholes","Weiner process","Mathematical finance","Finance and Financial Management","Mathematics","Other Mathematics","Physical Sciences and Mathematics"],"dc:title":["The Distribution of Individual Stock Returns in a Modified Black-scholes Option Pricing Model"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:41Z"}