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Optimal hitting time and perpetual option in a non-Lévy model: application to real options

Barrieu, Pauline and Bellamy, N. (2007) Optimal hitting time and perpetual option in a non-Lévy model: application to real options. Advances in Applied Probability, 39 (2). pp. 510-530. ISSN 0001-8678

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Identification Number: 10.1239/aap/1183667621


We study the perpetual American option characteristics in the case where the underlying dynamics involve a Brownian motion and a point process with a stochastic intensity. No assumption on the distribution of the jump size is made and we work with an arbitrary positive or negative jump. After proving the existence of an optimal stopping time for the problem and characterizing it as the hitting time of an optimal boundary,we provide closed-form formulae for the option value, as well as for the Laplace transform of the optimal stopping time. These results are then applied to the analysis of a real option problem when considering the impact of a fundamental and brutal change in the investment project environment. The consequences of this impact, that can seriously modify, positively or negatively, the project’s future cash flows and therefore the investment decision, are illustrated numerically via the study of some examples.

Item Type: Article
Official URL:
Additional Information: © 2007 Applied Probability Trust
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 28 May 2008 09:46
Last Modified: 20 Feb 2021 01:50

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