Real Options with Random Controls and the Value of Learning

In this paper we propose a conceptual framework for continuous-time valuation of real (investment) options in the presence of costly controls with random outcomes (learning), that affect the value of the underlying asset or a relevant state-variable. These controls represent optional efforts by management to add value to the underlying real investments over which it has monopoly power, albeit with uncertain results. Special cases of such controls include pure learning (but costly) actions, as in many research and development, marketing research or natural resource exploration projects. We demonstrate a discrete-time Markov-chain solution methodology implemented in a finite-difference scheme, and we discuss numerical results. The impact of such uncertain jumps is seen to be relatively more significant in the case of non-profitable options than in the case of very profitable real (investment) options. When the potential for information revelation is significant, we are even willing to pay for an action with a negative expected outcome. With numerical simulations we capture the value of embedded exploration (pure learning) options and we demonstrate the improvement over the traditional (sequential/compound) real options approach. We show that such exploration options enhance the value of investment opportunities in the most significant manner, and justify the (mostly unexplained) observed practice of overpaying for the purchase of rights to natural resources extraction.