#### Abstract

An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the option if the stock price is less than 12 because it will not be proﬁtable. This situation illustrates that there is a ﬁnancial advantage to owning options. Thus, options are not handed out for free. This Independent Study introduces a model called the binomial asset pricing model that can be used to price options. Also, it explores certain mathematical properties necessary to the pricing process, such as sigma-algebras, measurability, conditional expectation, and martingales. The ﬁnal chapter compares a real-world option price with the price given by the binomial model as well as applying the model in a completely different context—determining whether or not selected players from the 2003 NBA draft were worth their rookie salaries.

#### Advisor

Wooster, Robert

#### Department

Mathematics

#### Recommended Citation

Snyder, Ryan F., "Keeping Your Options Open: An Introduction to Pricing Options" (2014). *Senior Independent Study Theses.* Paper 5723.

http://openworks.wooster.edu/independentstudy/5723

#### Disciplines

Other Mathematics

#### Publication Date

2014

#### Degree Granted

Bachelor of Arts

#### Document Type

Senior Independent Study Thesis Exemplar

© Copyright 2014 Ryan F. Snyder