Valuing Future Information Under Uncertainty Using Polynomial Chaos
Résumé
This paper estimates the value of information for highly uncertain projects whose decisions have long-term impacts. We present a mathematically consistent framework using decision trees, Bayesian updating, and Monte Carlo simulation to value future information today, even when that future information is imperfect. One drawback of Monte Carlo methods in multivariate cases is the large number of samples required, which may result in prohibitive run times when considerable computer time is required to obtain each sample, as it is in our example. A polynomial chaos approach suitable for black-box functions is used to reduce these computations to manageable proportions. To our knowledge, this is the first exposition of polynomial chaos in the valuation literature. In our example it provides a speed-up of more than two orders of magnitude. We demonstrate the approach with an oilfield example involving a future decision on where to place a new injection well relative to a fault. The example considers the value to the asset holder of a measurement, to be made in the future, that reveals the degree of reservoir compartmentalization caused by this fault. In conditions of high demand for rigs and other scarce capital-intensive oilfield equipment, it may be appropriate for the asset holder to agree to a forward contract for this critical measurement to be taken at a future date at some specified price. The service provider would be contractually bound to provide this measurement at this pre-agreed price within a specified time window, regardless of the prevailing price and availability of rigs and equipment. Despite the presence of financial uncertainty on future oil price and private uncertainty on reservoir variables that are largely unresolved by the measurement, our methodology provides a computationally efficient valuation framework, possibly leading to novel ways of setting up contract terms.