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Options Réelles et Options Exotiques, une Approche Probabiliste

Abstract : This work focuses on valuing and hedging financial options that are not traded, called real options, and that are used to assess corporations' optimal capital investment decisions. For a company, the existence of an investment project is similar to owning a financial option: the company possesses the option to wait for the most favorable time to launch its project. Assessing the economic attractiveness of a project therefore requires to value this option. Our objective is to show how real option theory can benefit from exotic options methods. Unlike the classical approach in real options, which favors using differential equations techniques, we propose to value investment projects with probabilistic methods. This distinction allows not only to generalize the approach, but also to obtain analytical results in cases when a differential equation approach would not prove tractable. Also, it relates a corporate finance research domain with the very flourishing field of exotic options, a field where most results are obtained through probabilistic tools. Specifically, we first tackle the valuation of investment projects when there is a delay between the decision to invest and its actual implementation, when there is a competition between two economic agents with different delay-related constraints, and when the information available to the firm is noisy. We also look at the hedging of investment projects: how to hedge real options in the most efficient manner when there are transaction costs on the underlying assets, and how a new class of derivatives products that are related to barrier options allow to hedge the risk related to exercising real options. Finally, we focus on the optimal investment decision of an agent who has an impact on the market. An economic agent possessing privileged information on a company can trade its stock with profit, while pushing the market price towards the price that reflects the information. What is the agent's optimal strategy? The mathematical tools used are essentially probability, the theory of excursions, local times, and stochastic control. Several new results are shown, in particular regarding Brownian hitting times and excursion theory.
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Contributor : Laurent Gauthier Connect in order to contact the contributor
Submitted on : Friday, January 3, 2003 - 5:45:41 PM
Last modification on : Friday, April 29, 2022 - 10:12:05 AM
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  • HAL Id : tel-00002076, version 2



Laurent Gauthier. Options Réelles et Options Exotiques, une Approche Probabiliste. Mathématiques [math]. Université Panthéon-Sorbonne - Paris I, 2002. Français. ⟨tel-00002076v2⟩



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