A fuzzy approach to real option valuation

To have a real option means to have the possibility for a certain period to either choose for or against making an invetsment decision, without binding oneself up front. The real option rule is that one should invest today only if the net present value is high enough to compensate for giving up the value of the option to wait. Because the option to invest loses its value when the investment is irreversibly made, this loss is an opportunity cost of investing. The main question that a management group must answer for a deferrable investment opportunity is: How long do we postpone the investment, if we can postpone it, up to T time periods? In this paper we shall introduce a (heuristic) real option rule in a fuzzy setting, where the present values of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers. We shall determine the optimal exercise time by the help of possibilistic mean value and variance of fuzzy numbers. 1 Probabilistic real option valuation Options are known from the financial world where they represent the right to buy or sell a financial value, mostly a stock, for a predetermined price (the exercise price), without having the obligation to do so. The actual selling or buying of the underlying value for the predetermined price is called exercising your option. One would only exercise the option if the underlying value is higher than the exercise price in case of a call option (the right to buy) or lower than the exercise prise in the case of a put option (the right to sell). In 1973 Black and Scholes [4] made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative security dependent on a non-dividend paying stock. For risk-neutral investors the Black-Scholes pricing formula for a call option is C0 = S0N(d1)−XeN(d2), ∗The final version of this paper appeared in: Fuzzy Sets and Systems, 139(2003) 297-312.