Real Options Applied to Infrastructure Investments : A Volatility-Free Framework Based on Closed-Form Expressions

We derive closed-form expressions to price European calls and puts assuming the cash flows of the underlying asset or project are normally distributed. This approach has important advantages in the context of real options applied to infrastructure projects when compared to the Black-Scholes equation. First, it fits naturally with the way engineers and project managers evaluate projects, that is, based on cash flow estimates, and not on return estimates. And second, it does not require to estimate the volatility of geometric (not arithmetic) returns, a concept alien to project management. Two examples, an option to expand and an option to abandon, demonstrate the usefulness of this approach. A third example demonstrates the shortcomings of the Black-Scholes equation when applied to real assets