Real options and exotic options, a probabilistic approach.

Summary This book focuses on the valuation and hedging of non-market financial options, the real options, which are used to evaluate optimal investment decisions. The objective of this thesis is to show how real options theory benefits from the contributions of probabilistic methods used for exotic options. The classical approach to real options favors the use of differential equation techniques, and we propose to evaluate investment projects by applying highly probabilistic methods. This distinction allows us to generalize the classical approach to the problem, and to obtain analytical results in situations where a differential equation technique would not allow it. We address the valuation of investment projects under certain specific constraints: when there is an incompressible time lag between the decision and its implementation, when there is competition between actors with different characteristics, and when the market information is imperfect. We also study hedging problems: how to hedge complex real options in the most efficient way when there are transaction costs, and how a new class of derivatives that are similar to barrier options can hedge the risk associated with the exercise of real options. Finally, we consider the optimal investment decision when the market can be manipulated. An economic agent with privileged information can intervene in the market and influence the value of securities. The mathematical tools used are mainly probabilistic, mainly excursion theory, local time and stochastic control. Several new results are demonstrated, in particular concerning Brownian transit times and excursion theory.