Abstract

This thesis presents
efficient probabilistic
algorithms
for the pricing
of multiple exercise options.
The algorithms
handle the large class of
of constrained
multiple exercise American options.
Two algorithms are presented.
Single Pass Lookahead Search
provides a lower estimate
of an option price,
while
Nearest-Neighbor Martingale
provides
an upper estimate.
The convergence
of the algorithms
is proved
through
a Vapnik-Chernovenkis dimension analysis.
Their efficiency
is illustrated
on several examples,
including
a swing option with four constraints,
and a passport option
with 16 constraints.
The algorithms
are also applied
to the pricing
of equity-linked product
offering a reinvestment option.