University of Northern Iowa REU Projects

The University of Northern Iowa offers Alliance students the opportunity to participate in the summer research program under the workshop project format. Students will take the Mathematics of Financial Derivatives Workshop (taught by Professor Osvaldo Mendez) for approximate 4 weeks, and this will feed into one of the three research projects taught by faculty (to be named). UNI will host 9 students this summer with full accommodations and travel provided.

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Project 1

In the 1970’s Black and Scholes introduced their celebrated model which is today central to the pricing of derivative securities. Among other assumptions, they considered the case where the logarithm of the underlying price follows a Wiener Process with volatility. Since then, their model has been generalized in various directions, in particular to the case of the underlying price volatility not being constant. The project will focus on obtaining an expression for the price of a European option on a dividend-paying stock assuming the underlying price to have stochastic volatility.

Project 2

Different types of stock option lead to compatible boundary conditions for the Black-Scholes equation. Students will be working on a generalization of the Black-Scholes formula for different types of exotic options under more general assumptions on the underlying.

Project 3

Students will study the Black-Scholes Analysis under the assumption of the Underlying following a Levy Process. The possibility of more general stochastic processes for the underlying will be analyzed.

The Mathematics of Financial Derivatives

Mentor: Osvaldo Mendez

The focus of this workshop is to introduce the students to the theoretical and practical aspects of the mathematics of financial derivatives.

The analytic treatment of financial derivatives has attracted the attention of mathematicians and practitioners alike. Bachelier provided a mathematical model for the pricing of a special class of such derivatives in the early 20th century. Black and Scholes based his groundbreaking model on Bachelier’s work, in the early 1970’s.

In the course of this workshop, participants will learn the foundations of Probability Theory (probability spaces, random variables, stochastic differential equations, Brownian motion) and get acquainted with the basic notions of financial derivatives, such as futures and options. The theoretical machinery will then be applied to the study of the Black-Scholes model and to derive the Black-Scholes differential equation.

In the projects associated to the workshop, participants will work on a generalization of the Black-Scholes formula to the case in which the dividend-paying underlying’s volatility is stochastic.