Generalised soft multi-mode real options model (fuzzy-stochastic approach)

Abstract

Researchers and practitioners are dealing intensively with the real option valuation. One of the generalised types is reversible the multi-mode American real options. These options are solved mainly by applying the stochastic discrete binomial models. Uncertainty is a typical feature of valuation, and two basic types of representation are distinguished: risk (stochastic) and imprecision (fuzzy). The fuzzy-stochastic models indicate the generalised real options modelling containing both aspects. The objective of the paper is to develop and apply the generalised fuzzy-stochastic multi-mode real options model. This model is based on fuzzy numbers, the discrete binomial model, and the decomposition principle. Input data, particularly underlying cash-flows, are given by fuzzy-random numbers; fuzzy numbers give terminal values, risk-free rate, switching cost. Furthermore, assumptions and computation procedures are also described. The proposed optimisation problem is used for the fuzzy multi-mode real option value calculation. Results are compared with sub-problems, crisp-stochastic multi-modes real options and partial fuzzy-stochastic multi-mode real options models. A stylised illustrative operational flexibility example of comparing the fuzzy-stochastic multi-mode real options models is presented and discussed. The model can serve to valuation, decision-making, generalised sensitivity analysis and control under a fuzzy-stochastic environment.