Technical uncertainty in real options with learning

Sebastian Jaimungal; Ali Al-Aradi; Álvaro Cartea

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We introduce a new approach for incorporating technical uncertainty into the decision to invest in a commodity reserve by adopting a continuous-time Markov chain to model the reserve volume estimate. Learning is modeled by a decay in the rate of transitions among states that represent different reserve estimates.
A numerical scheme for pricing the real option with irreversible investment is given along with a relatively simple calibration procedure is presented demonstrating how to estimate the model parameters associated with learning rates.
Some numerical experiments are conducted to investigate the features of the solution including the effect of learning on the value of the real option. As expected, the inclusion of learning increases the value of the option. Additionally, different learning rates lead to profound changes in the investor’s exercise boundary which in turn depends on the investor’s prevailing reserve estimate.

Abstract

We introduce a new approach for incorporating uncertainty in the decision to invest in a commodity reserve. An investment is an irreversible one-off capital expenditure, after which the investor receives a stream of cashflow from extracting the commodity and selling it on the spot market. The investor is exposed to price uncertainty as well as uncertainty in the amount of available resources in reserve (also known as “technical uncertainty”). They do, however, learn about the reserve levels over time and this is a key determinant in the decision to invest. To model the uncertainty surrounding the reserve levels and how the investor learns via estimates of the commodity in the reserve, we adopt a continuous-time Markov chain model; this allows us to value the option to invest in the reserve and to investigate the value of learning prior to investment.

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