Abstract:
In this dissertation we consider the valuation of discretely monitored barrier
options under the in nite element method. The in nite element method is
an extension to the standard nite element method that accepts problems
with unbounded spacial domains (such as the Black-Scholes PDE), without
resorting to domain truncation. The degeneracy of the Black-Scholes PDE
when the underlying asset reaches zero, requires that the method be formulated
within the context of weighted Sobolev spaces. We will demonstrate
the convergence of the proposed method and provide a rigorous investigation
into the underlying weighted Sobolev spaces in which the convergence is to
be demonstrated.
