Jacob Robert Pieniazek



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Pricing stock options has been a highly discussed topic in financial mathematics. Binomial Tree Models are the basis for pricing these stock options. Utilizing this model, it is rather simple to price European stock options—options that can only be exercised at the terminal time. However, it is markedly more difficult to price American options—options that can be exercised at any time before or at the terminal time. The focus of this research was to understand the mechanism by which to price European stock options and extrapolate this knowledge to calculating the more complex American options and understanding the behavior of the boundary upon which the American option will be exercised—the optimal exercise boundary. Utilizing Python programming software, we were able to effectively create an algorithm that can calculate the stock-price binomial tree, price both European and American options, and separate the region in which the American option will be exercised throughout the time period. This provides us with a conceptualization of the behavior of stock options, particularly American options, and a further understanding of the mechanism by which American options are priced.

Publication Date


Project Designation

Capstone Project

Primary Advisor

Dan Ren

Primary Advisor's Department



Stander Symposium project, College of Arts and Sciences

United Nations Sustainable Development Goals

Quality Education

Binomial Tree Model: Pricing European and American Stock Options