Relationship under Various Stochastic Processes

Conventional belief in a negative relationship between uncertainty and investment has dominated real options theory for a long time. These studies argue that increased uncertainty causes a decrease in the current level of investments by raising optimal investment trigger. This paper postulates an argument 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. To investigate the relationship between uncertainty and investment, a general approach of Monte Carlo simulation is developed to derive optimal investment trigger under various stochastic processes when the closed-form solution could not be readily obtained. The overall effect of uncertainty on investment may be interpreted by the probability of investing, and the main result finds that the relationship appears to be an inverted U-shaped curve between uncertainty and investment. The implication is that uncertainty does not always discourage investment even under several sources of uncertainty. Therefore, high-risk projects are not always dominated by low-risk projects because high-risk projects may induce investment due to the higher probability of investing.