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A Framework of Monte Carlo Simulation for Examining the Uncertainty-Investment Relationship

Authors: George Yungchih Wang

Abstract:

This paper argues that increased uncertainty, in certain situations, may actually encourage investment. Since earlier studies mostly base their arguments on the assumption of geometric Brownian motion, the study extends the assumption to alternative stochastic processes, such as mixed diffusion-jump, mean-reverting process, and jump amplitude process. A general approach of Monte Carlo simulation is developed to derive optimal investment trigger for the situation that the closed-form solution could not be readily obtained under the assumption of alternative process. The main finding is that the overall effect of uncertainty on investment is interpreted by the probability of investing, and the relationship appears to be an invested U-shaped curve between uncertainty and investment. The implication is that uncertainty does not always discourage investment even under several sources of uncertainty. Furthermore, high-risk projects are not always dominated by low-risk projects because the high-risk projects may have a positive realization effect on encouraging investment.

Keywords: real options, geometric Brownian motion, mixeddiffusion-jump process, mean- reverting process, jump amplitudeprocess

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062636

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