Real-option valuation in a finite-time, incomplete market with jump diffusion and investor-utility inflation

Abstract

We extend an existing numerical model (Grasselli (2011)) for valuing a real option to invest in a capital project in an incomplete market with a finite time horizon. In doing so, we include two separate effects: the possibility that the project value is partly describable according to a jump-diffusion process, and incorporation of a time-dependent investor utility function, taking into account the effect of inflation. We adopt a discrete approximation to the jump process, whose parameters are restricted in order to preserve the drift and the volatility of the project-value process that it modifies. By controlling for these low-order effects, the higher-order effects may be considered in isolation. Our simulated results demonstrate that the inclusion of the jump process tends to decrease the value of the option, and expand the circumstances under which it should be exercised. Our results also demonstrate that an appropriate selection of the time-dependent investor utility function yields more reasonable investor-behaviour predictions regarding the decision to exercise the option, than would occur otherwise.