Fuzzy Pay-Off Method for Real Option Valuation
Encyclopedia
Fuzzy Pay-Off Method for Real Option Valuation (or just Pay-off Method) (FPOM) is a new method for valuing
real options, created in 2008. It is based on the use of fuzzy logic
and fuzzy numbers for the creation of the pay-off distribution of a possible project (real option). The structure of the method is similar to the probability theory based Datar-Mathews method.
of project outcomes from project cash-flow scenarios given by the responsible project managers – then the probability weighted mean value of the positive outcomes is calculated and multiplied by the probability of the positive outcomes (%) over all of the outcomes (100%). The answer is real option value. The Datar-Mathews method is shown to correspond to the answer from the Black–Scholes model when the same constraints are used.
By contrast, the main observations of the fuzzy pay-off model are the following:
The real option formula can be written simply as ROV = (A(Pos)/(A(Pos)+A(Neg)) x E[A+], where A(Pos) refers to the area of the positive part of the fuzzy distribution, A(Neg) refers to the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+].
In other words, the real option value can be derived (without any simulation whatsoever) from the fuzzy NPV. These are the blocks that together make the (fuzzy) pay-off method for real option valuation.
Simulation is not an absolutely necessary step in the Datar-Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar-Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory. This means that the way the two models treat uncertainty is different.
without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options).
The method has been taken into use in some large international industrial companies for the valuation of research and development
projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments.
The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology
and at the Tampere University of Technology in Finland.
Valuation (finance)
In finance, valuation is the process of estimating what something is worth. Items that are usually valued are a financial asset or liability. Valuations can be done on assets or on liabilities...
real options, created in 2008. It is based on the use of fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
and fuzzy numbers for the creation of the pay-off distribution of a possible project (real option). The structure of the method is similar to the probability theory based Datar-Mathews method.
Method
The Datar-Mathews method uses a simulation to generate a probability distributionProbability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
of project outcomes from project cash-flow scenarios given by the responsible project managers – then the probability weighted mean value of the positive outcomes is calculated and multiplied by the probability of the positive outcomes (%) over all of the outcomes (100%). The answer is real option value. The Datar-Mathews method is shown to correspond to the answer from the Black–Scholes model when the same constraints are used.
By contrast, the main observations of the fuzzy pay-off model are the following:
- The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers
- The mean value of the positive values of the fuzzy NPVNet present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
is the possibilistic mean value of the positive fuzzy NPV values. - Real option value, ROV, calculated from the fuzzy NPV is the possibilistic mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV.
The real option formula can be written simply as ROV = (A(Pos)/(A(Pos)+A(Neg)) x E[A+], where A(Pos) refers to the area of the positive part of the fuzzy distribution, A(Neg) refers to the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+].
In other words, the real option value can be derived (without any simulation whatsoever) from the fuzzy NPV. These are the blocks that together make the (fuzzy) pay-off method for real option valuation.
Simulation is not an absolutely necessary step in the Datar-Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar-Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory. This means that the way the two models treat uncertainty is different.
Use of the method
The pay-off method for real option valuation is very easy to use compared to the previous real option valuation methods and it can be used with the most commonly used spreadsheet softwareSpreadsheet
A spreadsheet is a computer application that simulates a paper accounting worksheet. It displays multiple cells usually in a two-dimensional matrix or grid consisting of rows and columns. Each cell contains alphanumeric text, numeric values or formulas...
without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options).
The method has been taken into use in some large international industrial companies for the valuation of research and development
Research and development
The phrase research and development , according to the Organization for Economic Co-operation and Development, refers to "creative work undertaken on a systematic basis in order to increase the stock of knowledge, including knowledge of man, culture and society, and the use of this stock of...
projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments.
The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology
Lappeenranta University of Technology
The Lappeenranta University of Technology was established in 1969. The university campus is situated on the shore of lake Saimaa, about 7 kilometres away from the city center...
and at the Tampere University of Technology in Finland.