Optimality of the Financial Decision and the Theory of American and Exotic Options.

Summary This thesis examines financial decisions through the theory of American and Exotic options. First, we present a review of the literature on American-style options. The pricing of the standard American call option is revisited in order to provide the prerequisites. In the next step, a new type of option contract, called the Euro-American Strangle or Hybrid Strangle, has been introduced. Analytical formulas have been provided for their prices as well as their management parameters. A new method is proposed to compute the integrals that define the early exercise bounds. This method has been shown to be efficient, accurate and fast for pricing all types of Strangle and beyond. Next, we examined American-style Step options. We have shown that the properties of vanilla call options do not apply to Step options in certain situations. Valuation formulas and management parameters were determined. And finally, we considered the valuation of a firm holding simultaneously an option to abandon and an option to expand its activities under different market conditions (favorable or unfavorable). Critical decision thresholds were obtained. Analytical formulas for the value of the firm have been obtained. Simulations illustrate the behavior of these critical decision thresholds.