Real option valuation under incomplete markets via dynamic programming

A real option value is obtained as a bid price, the maximum price an agent is willing to pay given underlying investment opportunities, such as financial or real investments. For evaluations, agent’s multi-period utility function is employed in a multi-stage portfolio model. The bid price provides a unique real option value consistent with arbitrage pricing theory. Properties of exponential utility allow use of dynamic programming. Resulting real option values are independent of utility discounting factors. Under partially complete markets PCM, such results are well known. We generalize the results relaxing all market completeness assumptions. For further computational improvements, we also propose a locally complete market assumption LCM for which PCM is a special case. Such relaxation is important, if realizations of real option cash flow convey information on subsequent price processes of underlying assets; then PCM may be violated but LCM not. The approach is illustrated with examples in flexible manufacturing systems under PCM, LCM and without any completeness assumption. The results demonstrate vast computational savings in comparison with stochastic programming. Bid price principle is easy to explain to managers and spread sheet calculations suit for valuation.