Fuzzy Black and Scholes Real Options Pricing

Abstract

Giga-investments are very large projects with long life cycles, which make them both risk investments and endeavours built on imprecise and uncertain assumptions. Still, the classical approach to judging the profitability of the investments is the calculation of the net present values (NPV) of estimated cash flows. This involves the use of fairly precise numbers, which somehow are estimated for life cycles of 15-25 years in an uncertain context. Real option valuation (ROV) has been proposed as an alternative and complement to the NPV calculations. Flexibility introduced with the ROV methods can be used for strategic purposes and better investment decisions can be made, when there are some degrees of flexibility available for the process of deciding on investment alternatives. Still, the problem with unrealistic expectations on precision has not been solved. It appears clear that a high level of precision in cash flow estimates will be misleading for the decision makers, but the methods used have required the precision used. We introduce a new method, the fuzzy ROV (or FROV), which is built on the use of fuzzy numbers and possibility distributions, and which has the capability to tackle imprecision and uncertainty in a direct and explicit way.