Valuation of real options in incomplete models – An implied yield approach

In many applications of real options there is an assumption of complete capital markets. For the perpetual timing option this means that if the underlying asset does not pay out any cash flows, then there is no finite optimal time at which the investment should be undertaken. In contrast, when the market is incomplete there is a possibility of having a finite optimal stopping time even in the cases when the underlying asset does not pay out any cash flows. We discuss the incomplete case in models driven by both Brownian motion(s) and a Poisson process and connect it with the concept of an implied yield. The implied yield will in these models extend the concept of a monetary yield (i.e. a yield that represents the fraction of the value of an asset paid out as a cash flow). Several examples of incomplete market models where there could be a finite optimal time to invest are given.