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When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.
Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.
This thesis presents efficient probabilistic algorithms for the pricing of multiple exercise options. The class of multiple exercise options handled by our algorithms is the class 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.