Date of Award
Master of Science
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.
Fertig, Laszlo Nicolai, "Numerical Solution of a Class of Stochastic Functional Differential Equations with Financial Applications" (2020). Theses and Dissertations. 2373.