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Published17 Jun 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 method of real options in publishing quite complex mathematics involved. Recent advances in modeling and analysis methods have made real option valuation easier to understand and to implement.

Types of real options[ edit ] Simple Examples Investment This simple example shows the relevance of the real option to delay investment and wait for further information, and is adapted from "Investment Example". Consider a firm that has the option to invest in a new factory.

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. In other words, real option valuation is treating investment opportunities and the different types of managerial flexibility as options and valuing them with option valuation models. Real options are useful both, as a mental model for strategic and operational decision-making, and as a valuation and numerical analysis tool.

This paper concentrates on the use of real options in numerical analysis, and particularly on the derivation of the real option value for a given investment opportunity, or identified managerial flexibility. 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 [ method of real options in publishing ], with the binomial option valuation method [ 3 ], with Successful options trading methods [ 4 ], and with a number of later methods based on these.

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.

A real option is an economically valuable right to make or else abandon some choice that is available to the managers of a company, often concerning business projects or investment opportunities. Real options differ thus from financial options contracts since they involve real i. Key Takeaways A real option gives a firm's management the right, but not the obligation to undertake certain business opportunities or investments. Real option refer to projects involving tangible assets versus financial instruments.

Recently, a novel approach to real option valuation, called the Datar-Mathews method DMM was presented in [ 5 — 7 ], where the real option value is calculated from a pay-off distribution, derived from a probability distribution of the net present value NPV for a project that is generated with a Monte-Carlo simulation.

The authors show that the results from the method converge to the results from the analytical Black-Scholes method.

The method presented greatly simplifies the calculation of the real option value, making it more transparent and brings real option valuation as a method a big leap closer to practitioners. The most positive issue in the DMM is that it does not suffer from the problems associated with the assumptions connected to the market processes connected to the Black-Scholes and the binomial option valuation methods.

The DMM utilizes cash-flow scenarios as an input to a Monte Carlo simulation to derive a distribution for the future investment outcomes.

• Project Valuation Using Real Options
• Real Options Selected Bibliography: Other Books.

This distribution is then used to create a pay-off distribution for the investment. The DMM is highly compatible with the way cash-flow-based profitability analysis is commonly done in companies, because it can use the same type of inputs as NPV analysis.

All of the afore-mentioned models and methods use probability theory in their treatment of uncertainty, there are, however, other ways than probability to treat uncertainty, or imprecision in future estimates, namely, fuzzy logic and fuzzy sets. In classical set theory an element either fully belongs to a set or does not belong to a set at all.

Table of Contents About the Item Business leaders are frequently faced with investment decisions on new and ongoing projects. The challenge lies in deciding what projects to choose, expand, contract, defer, or abandon, and which method of valuation to use is the key tool in the process. This title presents a step-by-step, practical approach to real options valuation to make it easily understandable by practitioners as well as senior management. This systematic approach to project valuation helps you minimize upfront investment risks, exercise flexibility in decision making, and maximize the returns. Considered one of the greatest innovations of modern finance, the real options approach is based on Nobel-prize winning work by three MIT economists, Fischer Black, Robert Merton, and Myron Scholes.

Bivalue logic, however, presents a problem, because financial decisions are generally made under uncertainty. Uncertainty in the financial investment context means that it is in practice impossible, exante to give absolutely correct precise estimates of, for example, future cash-flows.

### Bibliographic Information

There may be a number of reasons for this, see, for example, [ 8 ], however, the bottom line is that our estimations about the future are imprecise. This means that fuzzy sets can be used to formalize inaccuracy that exists in human decision making and as a representation of vague, uncertain, or imprecise knowledge, for example, future cash-flow estimation, which human reasoning is especially adaptive to.

The origins of fuzzy sets date back to an article by Lotfi Zadeh [ 11 ] 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. In the following subsection we will shortly present fuzzy sets and fuzzy numbers and continue shortly on using fuzzy numbers in option valuation.

• Real Option Definition
• Real Options Illustrated | Linda Peters | Springer

We will then 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.

Fuzzy Sets and Fuzzy Numbers A fuzzy subset of a nonempty??