Date of Award

May 2020

Degree Type


Degree Name

Master of Science



First Advisor

Chao Zhu

Committee Members

Chao Zhu, Richard Stockbridge, David A Spade


financial, numerical, SDE, SFDE


After a brief review of the Euler and Milstein numerical schemes and their convergence results

for stochastic differential equations (SDEs) and stochastic functional differential equations

(SFDEs), the thesis next proposes two specific SFDEs. The classical Euler and Milstein

schemes are developed to find the numerical solutions of these SFDEs, which are then compared

with the Ornstein-Uhlenbeck and a modified Ornstein-Uhlenbeck processes. These

results are further used to build four different but related stochastic models for stock prices.

The fitness of these models is analyzed by comparing real market data. The thesis concludes

with a numerical study for option pricing for stock models with path dependent volatilities.

Included in

Mathematics Commons