Date of Award
2022
Publisher
North Dakota State University
Document Type
Master's Paper
Degree Awarded
Master of Science (MS)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
SenGupta, Indranil
Description
In this paper, we introduce Brownian motion, and some of its drawbacks in connection to the financial modeling. We then introduce geometric Brownian motion as the basis for European call option pricing as we navigate our way through the Black-Scholes-Merton equation. Lévy Processes round out the background information of the paper as we discuss Poisson and compound Poisson processes and the pricing of European call options using the stochastic calculus of jump processes. Ornstein-Uhlenbeck processes are then constructed. Finally we review and analyze the Barndorff-Nielsen and Shepard model. We provide its application to price European call options using the fast Fourier transform and the direct integration method.
Recommended Citation
Uden, Austin, "Stochastic Processes, and Development of the Barndorff-Nielsen and Shephard Model for Financial Markets" (2022). Mathematics. 24.
https://digitalcommons.ndsu.edu/mathematics/24
Rights
NDSU policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/32334