A Dynamic Programming Approach to Real Option Valuation in Incomplete Markets

This paper propose a dynamic programming approach to evaluate uncertain income streams from an investment opportunity in incomplete markets. It is argued that the idea of certainty equivalent (CE) is applied to value such an investment opportunity as well as real options. We show that two approaches to certainty equivalent, the buying price and the selling price approaches, are exactly equal in exponential utility, implying that CE is a fair value for both the buyer and the seller. Numerical techniques are developed to decompose income streams into hedged positions and smaller residuals for convenient computation. The study finds that the dynamic programming approach provides a major advantage over traditional discounted cash flow approach, in that management is not necessarily to estimate risk-adjusted discount rate, thus reducing the chance of making wrongful investment decisions.