We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process, which can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone sequence of lower bounds. In a case study, we demonstrate that the frequently used quasi-analytic method yields a suboptimal policy and an inaccurate value function. The proposed method is demonstrably correct, straightforward to implement, reliable in computation, and broadly applicable in analyzing multidimensional option-valuation problems.

We derive an optimal decision rule with regards to making an irreversible switch from oil to gas production. The approach can be used by petroleum field operators to maximize the value creation from a petroleum field with diminishing oil production and remaining gas reserves. Assuming that both the oil and gas prices follow a geometric Brownian motion we derive an analytical solution for the exercise threshold. We also propose an explicit solution for the option value that is new to the literature. Numerical examples are used to demonstrate the threshold and option value for a generic petroleum field. Both the threshold and option value solutions are relevant for application to other real options cases with similar features (e.g. other types of switching options or a perpetual spread option).

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