Abstract
Real option analysis offers interesting insights on the value of assets and on the profitability of investments, which has made real options a growing field of academic research and practical application. Real option valuation is, however, often found to be difficult to understand and to implement due to the quite complex mathematics involved. Recent advances in modeling and analysis methods have made real option valuation easier to understand and to implement. This paper presents a new method (fuzzy pay-off method) for real option valuation using fuzzy numbers that is based on findings from earlier real option valuation methods and from fuzzy real option valuation. The method is intuitive to understand and far less complicated than any previous real option valuation model to date. The paper also presents the use of number of different types of fuzzy numbers with the method and an application of the new method in an industry setting.
Highlights
Real option valuation is based on the observation that the possibilities financial options give their holder resemble the possibilities to invest in real investments and possibilities found within real investments, that is, managerial flexibility: “an irreversible investment opportunity is much like a financial call option” 1
Real options are commonly valued with the same methods that have been used to value financial options, that is, with Black-Scholes option pricing formula 2, with the Journal of Applied Mathematics and Decision Sciences binomial option valuation method 3, with Monte-Carlo-based methods 4, and with a number of later methods based on these
We will present a new method for valuation of real options from fuzzy numbers that is based on the previous literature on real option valuation, especially the findings presented in 5 and on fuzzy real option valuation methods, we continue by illustrating the use of the method with a selection of different types of fuzzy numbers and with a case application of the new method in an industry setting, and close with a discussion and conclusions
Summary
Real option valuation is based on the observation that the possibilities financial options give their holder resemble the possibilities to invest in real investments and possibilities found within real investments, that is, managerial flexibility: “an irreversible investment opportunity is much like a financial call option” 1. Most of the methods are complex and demand a good understanding of the underlying mathematics, issues that make their use difficult in practice In addition these models are based on the assumption that they can quite accurately mimic the underlying markets as a process, an assumption that may hold for some quite efficiently traded financial securities, but may not hold for real investments that do not have existing markets or have markets that can by no means be said to exhibit even weak market efficiency. The origins of fuzzy sets date back to an article by Lotfi Zadeh where he developed an algebra for what he called fuzzy sets This algebra was created to handle imprecise elements in our decision-making processes, and is the formal body of theory that allows the treatment of practically all decisions in an uncertain environment. We will present a new method for valuation of real options from fuzzy numbers that is based on the previous literature on real option valuation, especially the findings presented in 5 and on fuzzy real option valuation methods, we continue by illustrating the use of the method with a selection of different types of fuzzy numbers and with a case application of the new method in an industry setting, and close with a discussion and conclusions
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