Samantha Lopez

Summer Science Abstract

My research area will be in financial mathematics. Financial mathematics is primarily about financial models and their use in the valuation of financial derivatives. Financial derivatives are instruments whose values are based on that of one or more underlying assets, such as stocks, commodities and currencies.

The focus of my research will be the valuation of various types of options in the generalized N-period binomial model. The N-period binomial model is a lattice-based model of the varying price of a stock or asset over time. In each time period we assume that there are only two possible directions that the stock price can go: either up or down and not remain the same. An option is the right to buy or sell an asset. There are many different types of options within two different categories: Vanilla and Exotic options. A call option is the right to buy an asset at a certain price (called strike or exercise price) at a certain date (expiration date). A put option is the right to sell an asset at a certain price at a certain date. European options are options that can only be utilized at expiration. American options are options that can be exercised at any time prior to, and including, expiration. American and European call and put options are referred to as Vanilla options. All other options are considered Exotic options. Exotic options include Look-Back options and Barrier options. Look-Back options when utilized, the dealer must pay the holder of the option the maximum value of a stock over a time at a specified expiration date. Barrier options have two categories: down-and-out or up-and-out. A down-and-out barrier option means that if the stock price falls blow the “barrier-price” then the option is rendered useless. An up-and-out barrier option means that if the stock price goes above the “barrier-price” then the option is rendered useless. There are also up-and-in and down-and-in options as well.

I will derive appropriate formulas for pricing various types of options in this model, and I will utilize the computer to find fair prices of these options using publicly available data corresponding to different stocks. Moreover, I will learn to use LaTeX, which is a document markup language and program. TeX is a typesetting system that assists in producing high-quality technical books and papers. It’s extremely useful to use in order to write complex equations.