Risk-Neutral Option Pricing Methods for Adjusting Constrained Cash Flows

Standard procedures for evaluating future cash flows are to find an appropriate discount rate consistent with the cash flow's risk and then to derive a present value. While discounted cash flows seem appropriate for many instances, finding appropriate discount rates is often difficult, or discount rates may not exist when the risk is actually a function of a decision that requires the cash-flow valuation. We consider two approaches that have been suggested to alleviate this problem: the capital asset pricing model (CAPM) and the risk-neutral pricing arguments from option theory. We discuss the assumptions inherent in these models and show the results on the well-known news vendor model. Our option pricing results correspond to Singhal's [17] results using CAPM and a different valuation procedure for the option pricing model. We, however, derive a simpler expression that clearly illustrates differences from the standard form ignoring risk.