Application of the fuzzy–stochastic methodology to appraising the firm value as a European call option

The valuing of a firm equity as a call option is a crucial problem in financial decision-making. There are two basic aspects that are studied; contingent claim features (payoff functions) and risk (stochastic process of underlying assets). However, non-preciseness (vagueness, uncertainty) of input data is often neglected. Thus, a combination of risk (stochastic) and uncertainty (fuzzy instruments) could be a useful approach in calculating a firm value as a call option. The Black–Scholes methodology of appraising equity as a European call option is applied. Fuzzy–stochastic methodology under fuzzy numbers (T-numbers) is proposed and described. Fuzzy–stochastic model of appraising a firm equity is proposed. Input data are in a form of fuzzy numbers and result, firm possibility–expected equity value is also determined vaguely as a fuzzy set. Illustrative example is introduced.