Ziyi Yan
Advisor: Prof. Leslie Cheng
Department: Mathematics

Geometric Brown Motion Model in the Financial Market

My independent research is in the area of financial mathematics. Financial mathematics is a field of applied mathematics, which analyzes and models the movements in the financial market. I am going to focus on the geometric Brownian motion model in the financial market. Geometric Brownian motion (GBM) is a special case of Brownian motion process and it plays a significant role in building a statistical model in the area of financial math. My research goal is to simulate the possible predicted value of a commodity, given its volatility rate, drift rate and the market’s fraction rate. I am going to use different programming languages, including R and Matlab, to do GBM simulation for some commodities and estimate the variations of GBM, which enables me to build confidence interval of predicted value. I will also develop a maximum likelihood estimation approach for the GBM modeling in the estimation process. In addition, my research project will cover some theoretical analysis of GBM.

I will consult several books and papers to help me be prepared with substantial knowledge of financial math. The books include An Undergraduate Introduction to Financial Mathematics by J. Robert Buchanan, Options, Futures and other Derivatives by John C. Hull, Brownian Motion and Stochastic Calculus by Ioannis Karatzas and Steven Shreve, An Introduction to Stochastic Modeling by Howard M. Taylor and Samuel Karlin and An Elementary Introduction to Mathematical Finance by Sheldon M. Ross.