Barrieu, Pauline and Bellamy, N.
Optimal hitting time and perpetual option in a non-Lévy model: application to real options.
Advances in applied probability, 39
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.
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