**Jennifer Hernandez**

**Mentor: Leslie Cheng**

**Valuation of Options**

Over the summer I will be conducting research in the field of financial mathematics with Professor Leslie Cheng. Since I have not taken any courses in financial math, I will begin by getting a grasp on some background knowledge. In order to learn the basics, I will use two books: *An Undergraduate Introduction to Financial Mathematics *by J. Robert Buchanan and *An Elementary Introduction to Mathematical Finance *by Sheldon M. Ross.

The research I will conduct will explore the valuation of options of various types of options. An option is the right- but not the obligation to- buy or sell an asset, such as a share of stock, at some agreed upon price (called the strike price) on some predetermined date in the future (called the maturity or expiration of the option). I will study two different kinds of options: European options and American options. The difference between the two is that a European option can only be exercised at maturity, while an American option can be exercised at or before the expiration date. Ultimately, my goal is to determine the fair price for these options. I will look at several different models, including the generalized binomial model and the Black-Scholes model and possibly others time permitting.