Award Date


Degree Type


Degree Name

Doctor of Philosophy in Mathematical Sciences


Mathematical Sciences

First Committee Member

Hongtao Yang, Chair

Second Committee Member

Michael Marcozzi

Third Committee Member

Pengtao Sun

Fourth Committee Member

Monika Neda

Graduate Faculty Representative

Seungmook Choi

Number of Pages



American options are the most commonly traded options in the market. They are used to mitigate risk, speculate about the future, and are the key components of complex trading strategies. In this dissertation, we propose a new front-fixing finite element method for the valuation of American options. One of the attractive qualities of our front-fixing finite element method is that the early exercise boundaries and the option prices can be computed simultaneously with very high accuracy.

We study in detail our front-fixing finite element method for the valuation of American options on stocks, American options on zero-coupon bonds under a class of one-factor models of the short interest rate, and American options on stocks under a regime-switching model. In all three cases we establish stability, present numerical results, examine our method, and compare it with others.


American option; Differential equations; Parabolic; Financial mathematics; Finite element method; Options (Finance) – Prices – Mathematical models; Parabolic partial differential equation; Regime-switching; Zero coupon bond