Abstract:
There exists no closed form approximation for arithmetically calculated Asian
options, but research has shown that closed form approximations are possible
for Geometrically calculated Asian options. The aim of this dissertation is to
effectively price American Asian options with the least squares Monte Carlo
approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences
and variance reduction techniques. We evaluate how these techniques affect
the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement
these techniques. We consider the effect of, Laguerre-, weighted Laguerre-
, Hermite-, and Monomial-basis functions on the Longstaff and Schwartz
(2001) model. We briefly investigate GPU optimization of the Longstaff and
Schwartz algorithm within Matlab. We also graph the associated implied
and Local volatility surfaces of the American Asian options to assist in the
practical applicability of these options.
