Abstract
This paper considers investment problems in real options with non-homogeneous two-factor uncertainty. We derive some analytical properties of the resulting optimal stopping problem and present a finite difference algorithm to approximate the firm’s value function and optimal exercise boundary. An important message in our paper is that the frequently applied quasi-analytical approach underestimates the impact of uncertainty. This is caused by the fact that the quasi-analytical solution does not satisfy the partial differential equation that governs the value function. As a result, the quasi-analytical approach may wrongly advise to invest in a substantial part of the state space.
Highlights
Since the seminal works of Dixit and Pindyck (1994) and Trigeorgis (1996), it has become clear that real investments should be valued using a real options approach when decision makers are exposed to a significant amount of uncertainty
The real options model consists of a single firm, having the opportunity to invest in a project of given size, with revenue that is subject to uncertainty, being governed by a single stochastic process
We find several papers concerning investment problems where the uncertainty is driven by multidimensional stochastic processes, and where no analytical solution can be derived
Summary
Since the seminal works of Dixit and Pindyck (1994) and Trigeorgis (1996), it has become clear that real investments should be valued using a real options approach when decision makers are exposed to a significant amount of uncertainty. This is revealed in these papers, because two processes (price/cost and cost) remain present in the equations For problems of this kind, Adkins and Paxson (2011b) propose a quasi-analytical approach that results in a set of equations to determine the optimal investment boundary. We refer to Heydari et al (2012), who extend the quasi-analytical approach proposed in Adkins and Paxson (2011b) to a three-factor model, which is employed to value the choice between two emission reduction technologies, assuming that the value of each option depends on fuel, electricity and CO2 prices, all following (correlated) Geometric Brownian motions. Most finite difference schemes have been developed to solve models with a one-dimensional stochastic process and a finite time horizon This method typically employs a backward induction argument in the time dimension to approximate the optimal exercise boundary and value function in a step-by-step fashion; see, e.g., (Dixit and Pindyck 1994, Appendix 10.A).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
