### by Bryce Runey

### Faculty mentor: Dr. Julius Esunge

In this research, we will look at derivatives as a function of accurately predicting risks and pricing. Both of which have the intention of either creating wealth monetarily, managing risks within respective industries, or in some fashions, a combination of both. Specifically, we will analyze the Greeks in the Black-Scholes equation and how they change the outcome of a call within the American markets. The project will involve analytical methods to derive and explain the usefulness of each of the Greeks. Also, statistical analysis will be performed on recent options data to show the practical aspects of each Greek. Mathematics, probability, and statistics are pivotal to accurately predicting both risks and pricing in these ubiquitous applications.