Fuzzy Volatility Effect on Major Projects Timing

Abstract

We determine the real option value and the optimal launching time of a major project when the project present value follows a stochastic process with fuzzy volatility, and the project has to be delayed until it is deemed financially or economically viable. When the volatility is a crisp value, it is known that the investment is triggered when the project present value hits a constant threshold, the investment trigger, strictly higher than the project investment cost to account for the loss of flexibility. We re-establish this rule when the volatility is a trapezoidal fuzzy number and discuss it with a numerical example. Because of the monotony of the investment trigger as a function of the volatility, the trigger membership function can be easily determined. Using a representative numerical example, we show in particular that the volatility ambiguity does not make the flexibility value to vanish. We show also that the investment trigger has rather a narrower core interval with respect to the fuzzy volatility core interval. To the best of our knowledge, this is the first continuous fuzzy real options model to address American option. The model can be used to introduce ambiguity surrounding the investment cost, present value or time-to- build of a given project and to investigate their impact on the project optimal launching date.