Real options valuation, also called real options valuation or real options analysis,[1] (ROV or ROA) is a business decision system. Applies financial option pricing techniques to decisions about material business assets.[2] A real option is the right, but not the obligation, to pursue business initiatives such as deferring, abandoning, expanding, arranging, or contracting a capital investment project.[3] For example, real options evaluation could examine both the possibility of investing in a factory expansion and the possibility of selling it.[4].
Real options are generally distinguished from conventional financial options in that they are not traded on an exchange.[5] Another distinction is that those who evaluate real options, usually the company's management, can directly influence the value of the project underlying the option, while this does not happen with the asset underlying a financial option. For example, a small tile company purchases a financial option to ensure the supply of natural gas during 2021 at a fixed amount. That company cannot influence the price of gas. But the company is also evaluating the real option of installing new machinery. The company can influence the price of that option, for example by choosing a cheaper machinery supplier.
Furthermore, management cannot measure uncertainty in terms of volatility (Volatility (Finance)), but must rely on its perceptions of uncertainty. Another difference with financial options (of which the market offers a wide catalog) is that the company's management also has to create or discover the real options available to it, and this process represents an important business task. Real options are all the more valuable the greater the uncertainty. Management has significant flexibility to change the course of the project in a direction it deems favorable.[6] The evaluation of real options is a recursive processː once an option is launched, new possibilities emerge within it. Continuing with the example of the tiler, once you have selected a supplier, they may offer you ovens of different powers, from which you will have to choose.
Real options analysis, as a discipline, extends from its application in corporate finance to decision making under uncertainty in general, adapting the techniques developed for financial options to “real life” decisions. For example, R&D managers can use real options pricing to deal with various uncertainties when making decisions about allocating resources among R&D projects.[7][8][9][10] Non-business examples might be evaluating the cost of cryptocurrency mining machines,[11] or a person's decision to start working for a company now, or giving up several years of income to attend graduate school.[12] Therefore, it requires decision-makers to be explicit about the assumptions underlying their projections. For this reason, ROV is increasingly employed as a tool in business strategy formulation.[13][14][15] This extension of real options to real-world projects often requires customized decision support systems, because otherwise complex composite options will become too unwieldy.[16].
Strategic investment evaluation
Introduction
Real options valuation, also called real options valuation or real options analysis,[1] (ROV or ROA) is a business decision system. Applies financial option pricing techniques to decisions about material business assets.[2] A real option is the right, but not the obligation, to pursue business initiatives such as deferring, abandoning, expanding, arranging, or contracting a capital investment project.[3] For example, real options evaluation could examine both the possibility of investing in a factory expansion and the possibility of selling it.[4].
Real options are generally distinguished from conventional financial options in that they are not traded on an exchange.[5] Another distinction is that those who evaluate real options, usually the company's management, can directly influence the value of the project underlying the option, while this does not happen with the asset underlying a financial option. For example, a small tile company purchases a financial option to ensure the supply of natural gas during 2021 at a fixed amount. That company cannot influence the price of gas. But the company is also evaluating the real option of installing new machinery. The company can influence the price of that option, for example by choosing a cheaper machinery supplier.
Furthermore, management cannot measure uncertainty in terms of volatility (Volatility (Finance)), but must rely on its perceptions of uncertainty. Another difference with financial options (of which the market offers a wide catalog) is that the company's management also has to create or discover the real options available to it, and this process represents an important business task. Real options are all the more valuable the greater the uncertainty. Management has significant flexibility to change the course of the project in a direction it deems favorable.[6] The evaluation of real options is a recursive processː once an option is launched, new possibilities emerge within it. Continuing with the example of the tiler, once you have selected a supplier, they may offer you ovens of different powers, from which you will have to choose.
Real options analysis, as a discipline, extends from its application in corporate finance to decision making under uncertainty in general, adapting the techniques developed for financial options to “real life” decisions. For example, R&D managers can use real options pricing to deal with various uncertainties when making decisions about allocating resources among R&D projects.[7][8][9][10] Non-business examples might be evaluating the cost of cryptocurrency mining machines,[11] or a person's decision to start working for a company now, or giving up several years of income to attend graduate school.[12] Therefore, it requires decision-makers to be explicit about the assumptions underlying their projections. For this reason, ROV is increasingly employed as a tool in business strategy formulation.[13][14][15] This extension of real options to real-world projects often requires customized decision support systems, because otherwise complex composite options will become too unwieldy.[16].
The adjective "real" in the expression "real option" does not mean what the RAE says, "that it has objective existence."[17] The eyes of the person who is reading this page are real in that sense: they exist, they can be touched, measured. If a company has a factory, the possible decision to expand or close it is, in financial language, a real option. It is before the decision is made, and whether it is made or not. But that name does not confer "reality." It remains a hypothesis. Nor does this adjective mean, as it is sometimes used in common language,[18] that it is a reasonable, or very probable, option among the existing ones. This adjective is used in the expression "real option" to distinguish it from the financial option, in a manner analogous to its use in the contrast between the real economy and the financial economy. Strictly speaking, the financial economy is as real (RAE) as the "real economy": there are banks and there are factories.
Types of real options
Contenido
La flexibilidad de la que dispone la dirección de la empresa –es decir, las "opciones reales"– genéricamente, se relacionará con el tamaño del proyecto, el momento del proyecto y la marcha del proyecto una vez se haya iniciado.[19] En todos los casos, cualquier gasto inicial (no recuperable) relacionado con esta flexibilidad es la prima de la opción. Las opciones reales también se aplican comúnmente a la valoración de acciones bursátiles.
Options related to project size
When the scope of the project is uncertain, flexibility in the size of relevant facilities is valuable and an option.[20].
• - Expansion option: The project is built with a production capacity greater than expected demand so that it can produce at a higher rate if necessary. Company management then has the option to increase production if conditions prove favorable. A project with an expansion option will cost more than one without (the difference is the option premium) but it will also be worth more. The extension option is, therefore, equivalent to a purchase option (call).
• - Reduction option: The project is designed in such a way that production can be reduced in the future if conditions turn out to be unfavorable. Exercising the option consists of giving up these future expenses. This is the equivalent of a put option and, again, the initial excess expense is the option premium.
• - Option to expand or reduce: the project is designed in such a way that it can be started or stopped as appropriate. Management can close part—or all—of the trade when conditions are unfavorable (put option) and can restart trades when conditions improve (call option). A good example is the flexible manufacturing system (FMS). This option is also known as switching option.
Options related to the life of the project and its scheduling
Where there is uncertainty about when and how commercial or other conditions will materialise, schedule flexibility for relevant projects is valuable and an option. Growth options are perhaps the most generic in this category. They involve the option of pursuing only those projects that appear to be profitable at the time of initiation.
• - Start or Postponement Options: Here management has flexibility regarding when to start a project. For example, in the exploitation of natural resources, a company can delay the extraction of a deposit until market conditions are favorable. This constitutes an American-style purchase option.
• - Delay option with a product patent: A company with a patent right on a product has the right to develop and market the product exclusively until the expiration of the patent (typically about 20 years from when the patent is applied for). The company will market and develop the product only if the present value of the expected cash flows from sales of the product exceeds the development cost. If this does not occur, the company can file the patent and not incur additional costs.
• - Abandonment option: Management may have the option to stop a project during its life and possibly obtain its salvage value. Here, when the present value of the remaining cash flows falls below the liquidation value, the asset can be sold, and this involves exercising a put option. This abandonment option is also known as Termination option. The dropout options are American style.
• - Sequencing options: this option is related to the previous start option, although it implies flexibility regarding the schedules of interrelated projects. In this case, the analysis must elucidate whether it is better to carry out the projects sequentially (mathematical succession) (one after the other) or in parallel (at the same time). For example, a mining company is considering building a train line to a port and some silos there. If the sequential option is chosen, by observing the results related to the first project, the company can remove some of the uncertainty related to the initiative as a whole. Once cleared, management has the option of whether or not to continue with the development of the other projects. If, on the other hand, the parallel option is chosen, when the first project is finished, the others will be advanced and money will have been spent on them, so the opportunity cost of not undertaking them is lost. Likewise, execution time is reduced, so the resulting assets will begin to produce benefits sooner. Project sequencing is important in corporate strategy. The notion of intraproject (within the same project) and interproject (between several projects) options is related to sequencing.
• - Prototyping option: some systems are incremental innovations of existing systems (whose functioning is well known), while others are radical innovations (which cannot be predicted how they will work). The latter are risky investments. Prototyping can cover some of these risks, because it costs much less than a full-scale system, and yet allows reliable information to be obtained about how that system would work economically and technically. In economic terms, prototyping is a risk hedging option (like the famous hedge options). This option has a cost that must be properly evaluated.[21] For example, new energy generation and storage systems are continually being developed due to climate change, resource scarcity and environmental laws.
Options related to project operation
Management may have flexibility regarding the products produced or the processes used in manufacturing. As in the previous cases, this flexibility increases the value of the project, corresponding in turn to the "premium" paid for the real option.
• - Product mix options: The option to produce different products from the same facility is known as product mix option or product flexibility. These options are particularly valuable in industries where demand is volatile or where total quantities demanded for a particular good are typically low, and management would want to switch to a different product quickly if necessary. An example is the nougat industry, with demand concentrated at Christmas, which can adapt its machinery to produce ice cream in the low season.[22].
• - Input Mixing Options: Also called process flexibility**,** this option allows management to use different inputs to produce the same result, as appropriate. For example, a farmer will consider the option of switching between several feed sources (hay, feed) and will prefer to use the cheapest acceptable alternative. An electric company may have the option to choose between several forms of electricity generation (hydroelectric, thermal).
• - Operational scale options: Management may have the option to change the quantity of production per unit of time, or change the total duration of production run time, for example, in response to market conditions. These options are also known as intensity options. They are very common in the automobile industryː if there is a lot of demand, a third shift is set up.[23].
Options valuation
Teniendo en cuenta lo anterior, está claro que existe una analogía entre las opciones reales y las opciones financieras,[24] y, por lo tanto, cabría esperar que para las primeras se pudieran aplicar modelos y análisis que llevan tiempo utilizándose en las segundas. Sin embargo, es importante entender por qué algunas técnicas estándar de valoración de opciones financieras pueden no ser aplicables para la valoración de opciones reales (ROV por sus siglas en inglés).[2].
Applicability of standard techniques
ROV is often contrasted with more standard capital budgeting techniques, such as discounted funds flow (DCF) analysis or net present value (NPV).[2] Under this "standard" NPV approach, expected future cash flows are valued in the present based on the measure of empirical probability at a discount rate that reflects the risk implicit in the project (see Financial Asset Pricing Model, Arbitrage Theory, and Weighted Average Cost of Capital). Only expected cash flows are considered here, without taking into account the "flexibility" to change corporate strategy based on actual behavior (see below also Corporate finance § Assessing flexibility).
The NPV framework assumes (implicitly) that management is “passive” with respect to its capital investment once committed. Some analysts take account of this uncertainty (i) by adjusting the discount rate, for example by increasing the cost of capital, or (ii) by adjusting cash flows, for example by using certainty equivalents, or (iii) by applying (subjective) "trims" to the forecast numbers, or (iv) through probability weighting of these as in rVAN.[25][26] However, even when the latter methods are employed, they typically do not take into account. adequately address changes in risk over the project life cycle and therefore fail to appropriately adapt risk adjustment.[27][28].
Instead, ROV assumes that management is “active” and can respond “continuously” to market changes. Real options evaluation considers "all" scenarios (or "states") and indicates the best corporate action in each of them.[29] Because management adapts to each negative outcome by decreasing its exposure, while adapting to positive scenarios by increasing its scale, the company benefits from the uncertainty in the underlying market, achieving lower earnings variability than with NPV analysis.
The contingent nature of future earnings in real options models is captured using techniques developed for financial options in the contingent rights analysis literature. The approach here, known as risk-neutral valuation, is to adjust the probability distribution to account for risk, while discounting at the risk-free rate. This technique, also known as the "martingale" approach (in Spanish one of the meanings of this word is "deception",[30] but originally martingale is a French game of chance that uses probability in a certain way), uses a measure of risk neutrality. For technical considerations see below.
Given these different treatments, the value of a project estimated with real options analysis is usually greater than that estimated with NPV, and the difference will be more marked in projects with greater flexibility, contingency and volatility.[31] This is analogous to financial options where a greater volatility of the underlying "Volatility (finance)") leads to a greater value (precisely financial options are to protect against this volatility, so that, the greater the volatility, the more expensive they cost).
An application of real options valuation in the Philippine banking industry showed that higher levels of income volatility can negatively affect the values of real options in the loan portfolio, when the presence of information asymmetry is considered. In this case, increased volatility can limit the value of a real option.[32].
Part of the criticism of real options pricing (and the subsequent slow adoption in practice and academia) comes from the generally higher values it yields for business assets. However, studies have shown that these values are reliable estimates, as long as the input data are appropriately identified.[33].
Options Based Valuation
Although there is much similarity between the modeling of real options and that of financial options,[24][34] ROV is distinguished from the latter in that it takes into account the uncertainty about the future evolution of the parameters that determine the value of the project, along with the capacity of management to respond to this evolution.[35][36].
It is the combined effect of this uncertainty and this capability that makes the ROV technically more complex than its alternatives. The full range of possible values for the asset must first be estimated. This involves estimating what its value would be if it existed today (usually it is a project, so it does not exist yet) and forecasting the set of possible future values. These calculations provide numbers for all possible option values at the different points where a decision is needed about whether to proceed with the project.
When valuing the real option, the analyst must therefore consider the factors (inputs) that affect the value of a real option, the valuation method used and whether technical limitations can be applied. Conceptually, the valuation of a real option analyzes the premium between what the company pays for a certain project and what that project yields (the money it gives). The factors that affect the value of a real option (time, interest rates, volatility, cash inflows and outflows) are affected by the business conditions and the environment in which the project operates. Business conditions (such as ownership information, data collection costs, or patents) depend on the political, environmental, sociocultural, technological, and legal situations affecting an industry.
Just as the environment affects business conditions, it also affects the volatility of returns, the interest rate and the projections of payments and returns of a project.[37].
Given the similarity in the valuation approach, the factors necessary to model the real option correspond to those necessary for the valuation of a financial option.[24][34][35] However, the specific application for real options is as follows:.
• - The underlying of the option is the project in question. It is modeled in terms of:
Spot price: The initial or present value of the project is required: this is usually based on management's "best guess" as to the gross cash flow value of the project and the resulting net present value;
Volatility "Volatility (finance)"): A measure of the uncertainty as to the change in value over time is required.
Generally, the volatility in the value of the project is used, normally obtained through the Monte Carlo method.[35][38] Sometimes the volatility of the cash flows of the first period is preferred[36] (see below in Corporate Finance for an explanation related to the estimation of the NPV and the volatility of the project).
Limitations
La relevancia de las opciones reales, incluso como marco mental, puede verse limitada debido a consideraciones de mercado, organizativas o técnicas.[48] Cuando se emplea el marco, por lo tanto, el analista debe considerar previamente lo siguiente para determinar si la ROV es relevante para el proyecto en cuestión.
Market characteristics
As already explained, the market and environment underlying the project must be those in which "change is most evident", and the "source, trends and evolution" in the supply and demand of the product create the "flexibility, contingency and volatility"[31] that result in optionality. In other cases it is better to use the VAN method.
Organizational considerations
Real options are "particularly important for companies with some key characteristics",[31] and may be less relevant in other cases.[36] In summary, it is important to consider the following in determining whether the ROV framework is applicable:.
The corporate strategy has to adapt to contingent events. Some corporations face organizational rigidities and cannot react to market changes; In this case, the NPV approach is more appropriate.
In practice, the company must be positioned in such a way that it has an adequate flow of information and opportunities to act. Often this will be a market leader or a company that enjoys economies of scale and scope.
Management must understand options, be able to identify and create them, and exercise them appropriately.[16] This contrasts with business leaders focused on maintaining the status quo or short-term accounting profits.
The financial position of the company must be such that it has the ability to finance the project when necessary (i.e., issue shares, take on more debt or use internally generated cash flow). Management must, therefore, have appropriate access to this capital.
Management must be able to exercise real options. Some may be exercised by a single party, while others may require the agreement of several.
Technical considerations
Limitations in the use of these models arise due to the contrast between real options and financial options, for which these models were originally developed. The main difference is that the underlying is often not tradable on a stock market – for example, the owner of the factory cannot sell it easily and quickly, as he can with a stock. Furthermore, the real option itself may also not be (in this stock market sense) negotiable – for example, the factory owner cannot sell the right to expand his factory to another party; only he can make this decision. However, some real options can be sold. For example, ownership of vacant land is a real option to develop it in the future. Even where a market exists – for the underlying or for the option – in most cases market liquidity is limited (or non-existent). Finally, even if the company can actively adapt to market changes, the correct paradigm for discounting future claims remains to be determined.
The difficulties are then:
As noted above, data issues arise regarding the estimation of key inputs to the model. In this case, since the value or price of the underlying cannot be observed (directly), there will always be uncertainty as to its value and volatility (in turn increased by uncertainty as to possible management actions in the future).
It is often difficult to grasp the rules for the exercise of each of the real options and the consequent actions by management. Furthermore, a project may have a broad set of real options, some of which may be mutually exclusive.[16].
Theoretical difficulties may also arise, which are more serious.
These problems are addressed through several interrelated assumptions:
As explained above, data problems are usually addressed through a simulation of the project or a proxy listed on some stock exchange. Several new methods—such as those described above—also address these issues.
Likewise, as noted above, specific exercise rules can often be accommodated by encoding them in a custom binomial tree.[49].
Theoretical problems:
History
Although business managers have made capital investment decisions for centuries, the term "real option" is relatively new and was coined by Professor Stewart Myers of the MIT Sloan School of Management in 1977. In 1930, Irving Fisher wrote explicitly about the "options" available to the owner of a business (The Theory of Interest, II. viii). However, the description of such opportunities as "real options" followed the development of analytical techniques (such as the Black-Scholes Model in 1973) for financial options. For this reason the term "real option" is closely linked to these techniques.
Real options are today an active field of academic research. Professor Lenos Trigeorgis has been a prominent name for many years and has published several influential academic books and articles. Other pioneering scholars in the field include Professors Michael Brennan, Eduardo Schwartz, Graham Davis, Gonzalo Cortazar, Han Smit, Avinash Dixit, and Robert Pindyck (the latter two authors of the pioneering text in the discipline). An academic conference on real options is organized annually (Annual International Conference on Real Options).
Among others, the concept was popularized by Michael J. Mauboussin, then chief US investment strategist for Credit Suisse First Boston.[31] He uses real options to explain the gap between how the stock market values some companies and the "intrinsic value (finance)" of those companies. Trigeorgis has also disseminated real options through articles (for laymen) in publications such as The Wall Street Journal.[29] This popularization is such that ROV is now a standard offering in graduate finance degrees and often even in MBA curricula at many business schools.
Recently, real options have been used in business strategy, both for valuation purposes and as a conceptual framework.[13][14] The idea of treating strategic investments as options was popularized by Timothy Luehrman[50] in two HBR articles:[24] "In financial terms, a business strategy is much more like a series of options than a series of static cash flows." Investment opportunities are plotted in an “option space” with dimensions of “volatility” and value-to-cost ratio (“NPVc”).
Luehrman also co-authored with William Teichner a Harvard Business School case study, Arundel Partners: The Sequel Project, in 1992, which may have been the first business school case study to teach ROV. Reflecting the "integration" of ROV, Professor Robert C. Merton discussed Arundel's essential points in the lecture he gave upon receiving the Nobel Prize in 1997.[52] Arundel involves a group of investors considering acquiring the rights to sequels to a portfolio of yet-to-be-released feature films. In particular, investors must determine the value of the rights to these sequels before any of the first films are produced. Here, investors are faced with 2 main options: they can produce an original film and a sequel at the same time or they can wait to decide on a sequel after the original film is released. The second approach, Merton says, provides the option of not shooting the sequel in the event that the initial film is not successful. This real option has economic value and can be valued monetarily using an option pricing model.
• - Kodukula, P., & Papudesu, C. (2006). Project valuation using real options: a practitioner's guide. J. Ross Publishing. ISBN 978-1932159431.
Applications:.
• - Grenadier, Steven R. & Weiss, Allen M., 1997. "Investment in technological innovations: An option pricing approach," Journal of Financial Economics, Elsevier, vol. 44(3), pages 397–416, June.
• - The Impact of Real Options in Agency Problems G. Siller-Pagaza, G. Otalora, E. Cobas-Flores (2006).
General
Theory
• - Introduction to real options valuation as a modeling problem Archived November 15, 2012 at the Wayback Machine., Mikael Collan.
• - The promise and peril of real options, Prof. Aswath Damodaran, Stern School of Business.
• - Real Options Tutorial, Prof. Marco Dias, PUC-Rio.
• - Valuation of real options: frequent errors, Prof. Pablo Fernández, IESE Business School, University of Navarra.
• - Identifying real options, Prof. Campbell R. Harvey. Duke University, Fuqua School of Business.
• - An introduction to real options Archived May 25, 2012 at the Wayback Machine. (Southern African Society of Investment Analysts), Prof. E. Gilbert, University of Cape Town.
• - Decision making under uncertainty: real options to the rescue?, Prof. Lucas Miller and Chan Park, Auburn University.
• - Real Options White Papers and Case Studies Archived February 8, 2012 at the Wayback Machine., Dr. Jonathan Mun.
• - Real options – Introduction, Portfolio Group.
• - How do you evaluate the value of a company's "real options"? Archived October 20, 2019 at the Wayback Machine., Prof. Alfred Rappaport Columbia University and Michael Mauboussin.
• - Some important issues involving real options: an overview, Gordon Sick and Andrea Gamba (2005).
• - Real Power of Real Options, Leslie and Michaels (1997), Keith Leslie and Max Michaels McKinsey Quarterly, 1997 (3) pages 4–22. Quoted by Robert Merton in his Nobel Prize acceptance speech in 1997. McKinsey Classic - Reprinted in McKinsey Anthology 2000 - On Strategy. Quoted in McKinsey Anthology 2011 - Have you tested your strategy lately?
Magazines
• - Real Options Magazine.
• - Magazine of Real Options and Strategy.
Calculation resources
• - ROV Spreadsheet Models, Prof. Aswath Damodaran, Stern School of Business.
• - Real Options Calculator, Prof. Steven T. Hackman, Georgia Institute of Technology.
[3] ↑ a b c Locatelli, Giorgio; Mancini, Mauro; Lotti, Giovanni (15 de abril de 2020). «A simple-to-implement real options method for the energy sector». Energy (en inglés) 197: 117226. ISSN 0360-5442. doi:10.1016/j.energy.2020.117226. Archivado desde el original el 4 de mayo de 2020.: http://eprints.whiterose.ac.uk/157998/
[6] ↑ Locatelli, Giorgio; Boarin, Sara; Pellegrino, Francesco; Ricotti, Marco E. (1 de febrero de 2015). «Load following with Small Modular Reactors (SMR): A real options analysis». Energy 80: 41-54. doi:10.1016/j.energy.2014.11.040.: http://eprints.whiterose.ac.uk/91139/1/Accpeted%20version.pdf
[9] ↑ Huang, Hsini; Jong, Simcha (2019). «Public Funding for Science and the Value of Corporate R&D Projects; Evidence from Project Initiation and Termination Decisions in Cell Therapy». Journal of Management Studies (en inglés) 56 (5): 1000-1039. ISSN 1467-6486. doi:10.1111/joms.12423.: https://es.wikipedia.org//portal.issn.org/resource/issn/1467-6486
[10] ↑ Gunther McGrath, Rita; Nerkar, Atul (January 2004). «Real options reasoning and a new look at the R&D investment strategies of pharmaceutical firms». Strategic Management Journal (en inglés) 25 (1): 1-21. ISSN 0143-2095. doi:10.1002/smj.358.: https://archive.org/details/sim_strategic-management-journal_2004-01_25_1/page/n3
[11] ↑ Yaish, Aviv; Zohar, Aviv (18 de junio de 2020). Pricing ASICs for Cryptocurrency Mining. arXiv:2002.11064.: http://arxiv.org/abs/2002.11064
[12] ↑ See Bilkic et al. under Real options valuation-Applications]].
[16] ↑ a b c Zhang, S.X.; Babovic, V. (2011). «An evolutionary real options framework for the design and management of projects and systems with complex real options and exercising conditions». Decision Support Systems 51 (1): 119-129. doi:10.1016/j.dss.2010.12.001.: https://www.researchgate.net/publication/220197192
[17] ↑ Real Academia Española. «real». Diccionario de la lengua española (23.ª edición).: https://dle.rae.es/real
[21] ↑ Lai, Chun Sing; Locatelli, Giorgio (February 2021). «Valuing the option to prototype: A case study with Generation Integrated Energy Storage». Energy 217: 119290. doi:10.1016/j.energy.2020.119290.: https://dx.doi.org/10.1016%2Fj.energy.2020.119290
[24] ↑ a b c d Timothy Luehrman: "Investment Opportunities as Real Options: Getting Started on the Numbers". Harvard Business Review 76, no. 4 (July – August 1998): 51–67.; "Strategy as a Portfolio of Real Options". Harvard Business Review 76, no. 5 (September–October 1998): 87-99.
[25] ↑ Ver: §32 "Certainty Equivalent Approach" & §165 "Risk Adjusted Discount Rate" in: Joel G. Siegel; Jae K. Shim; Stephen Hartman (1 de noviembre de 1997). Schaum's quick guide to business formulas: 201 decision-making tools for business, finance, and accounting students. McGraw-Hill Professional. ISBN 978-0-07-058031-2. Consultado el 12 de noviembre de 2011.: https://archive.org/details/schaumsquickguid00sieg
[32] ↑ Tan, Jackson J.; Trinidad, Fernando L. (15 de febrero de 2018). «A real options model for loan portfolios of actively traded Philippine universal banks». Journal of Global Entrepreneurship Research 8: 4. ISSN 2251-7316. doi:10.1186/s40497-018-0091-9.: https://es.wikipedia.org//portal.issn.org/resource/issn/2251-7316
[35] ↑ a b c Jenifer Piesse and Alexander Van de Putte. (2004). "Volatility estimation in Real Options". 8th Annual International Conference on Real Options.: http://www.financialcertified.com/article12.pdf
[41] ↑ Ver pág. 26 en Marion A. Brach (2003). Real Options in Practice. Wiley. ISBN 0471445568.
[42] ↑ a b See Ch. 23, Sec. 5, in: Frank Reilly, Keith Brown (2011). "Investment Analysis and Portfolio Management" (10th Edition). South-Western College Pub. ISBN 0538482389.
[43] ↑ Cortazar, Gonzalo; Gravet, Miguel; Urzua, Jorge (2008). «The valuation of multidimensional American real options using the LSM simulation method». Computers & Operations Research 35: 113-129. doi:10.1016/j.cor.2006.02.016.: http://www.gonzalocortazar.com/CortazarGravetUrzua2008.pdf
[45] ↑ Datar, V.; Mathews, S. (2004). «European Real Options: An Intuitive Algorithm for the Black Scholes Formula». Journal of Applied Finance 14 (1).
[47] ↑ Collan, M.; Fullér, R.; Mezei, J. (2009). «Fuzzy Pay-Off Method for Real Option Valuation». Journal of Applied Mathematics and Decision Sciences 2009 (13601): 1-15. doi:10.1155/2009/238196.: https://dx.doi.org/10.1155%2F2009%2F238196
The adjective "real" in the expression "real option" does not mean what the RAE says, "that it has objective existence."[17] The eyes of the person who is reading this page are real in that sense: they exist, they can be touched, measured. If a company has a factory, the possible decision to expand or close it is, in financial language, a real option. It is before the decision is made, and whether it is made or not. But that name does not confer "reality." It remains a hypothesis. Nor does this adjective mean, as it is sometimes used in common language,[18] that it is a reasonable, or very probable, option among the existing ones. This adjective is used in the expression "real option" to distinguish it from the financial option, in a manner analogous to its use in the contrast between the real economy and the financial economy. Strictly speaking, the financial economy is as real (RAE) as the "real economy": there are banks and there are factories.
Types of real options
Contenido
La flexibilidad de la que dispone la dirección de la empresa –es decir, las "opciones reales"– genéricamente, se relacionará con el tamaño del proyecto, el momento del proyecto y la marcha del proyecto una vez se haya iniciado.[19] En todos los casos, cualquier gasto inicial (no recuperable) relacionado con esta flexibilidad es la prima de la opción. Las opciones reales también se aplican comúnmente a la valoración de acciones bursátiles.
Options related to project size
When the scope of the project is uncertain, flexibility in the size of relevant facilities is valuable and an option.[20].
• - Expansion option: The project is built with a production capacity greater than expected demand so that it can produce at a higher rate if necessary. Company management then has the option to increase production if conditions prove favorable. A project with an expansion option will cost more than one without (the difference is the option premium) but it will also be worth more. The extension option is, therefore, equivalent to a purchase option (call).
• - Reduction option: The project is designed in such a way that production can be reduced in the future if conditions turn out to be unfavorable. Exercising the option consists of giving up these future expenses. This is the equivalent of a put option and, again, the initial excess expense is the option premium.
• - Option to expand or reduce: the project is designed in such a way that it can be started or stopped as appropriate. Management can close part—or all—of the trade when conditions are unfavorable (put option) and can restart trades when conditions improve (call option). A good example is the flexible manufacturing system (FMS). This option is also known as switching option.
Options related to the life of the project and its scheduling
Where there is uncertainty about when and how commercial or other conditions will materialise, schedule flexibility for relevant projects is valuable and an option. Growth options are perhaps the most generic in this category. They involve the option of pursuing only those projects that appear to be profitable at the time of initiation.
• - Start or Postponement Options: Here management has flexibility regarding when to start a project. For example, in the exploitation of natural resources, a company can delay the extraction of a deposit until market conditions are favorable. This constitutes an American-style purchase option.
• - Delay option with a product patent: A company with a patent right on a product has the right to develop and market the product exclusively until the expiration of the patent (typically about 20 years from when the patent is applied for). The company will market and develop the product only if the present value of the expected cash flows from sales of the product exceeds the development cost. If this does not occur, the company can file the patent and not incur additional costs.
• - Abandonment option: Management may have the option to stop a project during its life and possibly obtain its salvage value. Here, when the present value of the remaining cash flows falls below the liquidation value, the asset can be sold, and this involves exercising a put option. This abandonment option is also known as Termination option. The dropout options are American style.
• - Sequencing options: this option is related to the previous start option, although it implies flexibility regarding the schedules of interrelated projects. In this case, the analysis must elucidate whether it is better to carry out the projects sequentially (mathematical succession) (one after the other) or in parallel (at the same time). For example, a mining company is considering building a train line to a port and some silos there. If the sequential option is chosen, by observing the results related to the first project, the company can remove some of the uncertainty related to the initiative as a whole. Once cleared, management has the option of whether or not to continue with the development of the other projects. If, on the other hand, the parallel option is chosen, when the first project is finished, the others will be advanced and money will have been spent on them, so the opportunity cost of not undertaking them is lost. Likewise, execution time is reduced, so the resulting assets will begin to produce benefits sooner. Project sequencing is important in corporate strategy. The notion of intraproject (within the same project) and interproject (between several projects) options is related to sequencing.
• - Prototyping option: some systems are incremental innovations of existing systems (whose functioning is well known), while others are radical innovations (which cannot be predicted how they will work). The latter are risky investments. Prototyping can cover some of these risks, because it costs much less than a full-scale system, and yet allows reliable information to be obtained about how that system would work economically and technically. In economic terms, prototyping is a risk hedging option (like the famous hedge options). This option has a cost that must be properly evaluated.[21] For example, new energy generation and storage systems are continually being developed due to climate change, resource scarcity and environmental laws.
Options related to project operation
Management may have flexibility regarding the products produced or the processes used in manufacturing. As in the previous cases, this flexibility increases the value of the project, corresponding in turn to the "premium" paid for the real option.
• - Product mix options: The option to produce different products from the same facility is known as product mix option or product flexibility. These options are particularly valuable in industries where demand is volatile or where total quantities demanded for a particular good are typically low, and management would want to switch to a different product quickly if necessary. An example is the nougat industry, with demand concentrated at Christmas, which can adapt its machinery to produce ice cream in the low season.[22].
• - Input Mixing Options: Also called process flexibility**,** this option allows management to use different inputs to produce the same result, as appropriate. For example, a farmer will consider the option of switching between several feed sources (hay, feed) and will prefer to use the cheapest acceptable alternative. An electric company may have the option to choose between several forms of electricity generation (hydroelectric, thermal).
• - Operational scale options: Management may have the option to change the quantity of production per unit of time, or change the total duration of production run time, for example, in response to market conditions. These options are also known as intensity options. They are very common in the automobile industryː if there is a lot of demand, a third shift is set up.[23].
Options valuation
Teniendo en cuenta lo anterior, está claro que existe una analogía entre las opciones reales y las opciones financieras,[24] y, por lo tanto, cabría esperar que para las primeras se pudieran aplicar modelos y análisis que llevan tiempo utilizándose en las segundas. Sin embargo, es importante entender por qué algunas técnicas estándar de valoración de opciones financieras pueden no ser aplicables para la valoración de opciones reales (ROV por sus siglas en inglés).[2].
Applicability of standard techniques
ROV is often contrasted with more standard capital budgeting techniques, such as discounted funds flow (DCF) analysis or net present value (NPV).[2] Under this "standard" NPV approach, expected future cash flows are valued in the present based on the measure of empirical probability at a discount rate that reflects the risk implicit in the project (see Financial Asset Pricing Model, Arbitrage Theory, and Weighted Average Cost of Capital). Only expected cash flows are considered here, without taking into account the "flexibility" to change corporate strategy based on actual behavior (see below also Corporate finance § Assessing flexibility).
The NPV framework assumes (implicitly) that management is “passive” with respect to its capital investment once committed. Some analysts take account of this uncertainty (i) by adjusting the discount rate, for example by increasing the cost of capital, or (ii) by adjusting cash flows, for example by using certainty equivalents, or (iii) by applying (subjective) "trims" to the forecast numbers, or (iv) through probability weighting of these as in rVAN.[25][26] However, even when the latter methods are employed, they typically do not take into account. adequately address changes in risk over the project life cycle and therefore fail to appropriately adapt risk adjustment.[27][28].
Instead, ROV assumes that management is “active” and can respond “continuously” to market changes. Real options evaluation considers "all" scenarios (or "states") and indicates the best corporate action in each of them.[29] Because management adapts to each negative outcome by decreasing its exposure, while adapting to positive scenarios by increasing its scale, the company benefits from the uncertainty in the underlying market, achieving lower earnings variability than with NPV analysis.
The contingent nature of future earnings in real options models is captured using techniques developed for financial options in the contingent rights analysis literature. The approach here, known as risk-neutral valuation, is to adjust the probability distribution to account for risk, while discounting at the risk-free rate. This technique, also known as the "martingale" approach (in Spanish one of the meanings of this word is "deception",[30] but originally martingale is a French game of chance that uses probability in a certain way), uses a measure of risk neutrality. For technical considerations see below.
Given these different treatments, the value of a project estimated with real options analysis is usually greater than that estimated with NPV, and the difference will be more marked in projects with greater flexibility, contingency and volatility.[31] This is analogous to financial options where a greater volatility of the underlying "Volatility (finance)") leads to a greater value (precisely financial options are to protect against this volatility, so that, the greater the volatility, the more expensive they cost).
An application of real options valuation in the Philippine banking industry showed that higher levels of income volatility can negatively affect the values of real options in the loan portfolio, when the presence of information asymmetry is considered. In this case, increased volatility can limit the value of a real option.[32].
Part of the criticism of real options pricing (and the subsequent slow adoption in practice and academia) comes from the generally higher values it yields for business assets. However, studies have shown that these values are reliable estimates, as long as the input data are appropriately identified.[33].
Options Based Valuation
Although there is much similarity between the modeling of real options and that of financial options,[24][34] ROV is distinguished from the latter in that it takes into account the uncertainty about the future evolution of the parameters that determine the value of the project, along with the capacity of management to respond to this evolution.[35][36].
It is the combined effect of this uncertainty and this capability that makes the ROV technically more complex than its alternatives. The full range of possible values for the asset must first be estimated. This involves estimating what its value would be if it existed today (usually it is a project, so it does not exist yet) and forecasting the set of possible future values. These calculations provide numbers for all possible option values at the different points where a decision is needed about whether to proceed with the project.
When valuing the real option, the analyst must therefore consider the factors (inputs) that affect the value of a real option, the valuation method used and whether technical limitations can be applied. Conceptually, the valuation of a real option analyzes the premium between what the company pays for a certain project and what that project yields (the money it gives). The factors that affect the value of a real option (time, interest rates, volatility, cash inflows and outflows) are affected by the business conditions and the environment in which the project operates. Business conditions (such as ownership information, data collection costs, or patents) depend on the political, environmental, sociocultural, technological, and legal situations affecting an industry.
Just as the environment affects business conditions, it also affects the volatility of returns, the interest rate and the projections of payments and returns of a project.[37].
Given the similarity in the valuation approach, the factors necessary to model the real option correspond to those necessary for the valuation of a financial option.[24][34][35] However, the specific application for real options is as follows:.
• - The underlying of the option is the project in question. It is modeled in terms of:
Spot price: The initial or present value of the project is required: this is usually based on management's "best guess" as to the gross cash flow value of the project and the resulting net present value;
Volatility "Volatility (finance)"): A measure of the uncertainty as to the change in value over time is required.
Generally, the volatility in the value of the project is used, normally obtained through the Monte Carlo method.[35][38] Sometimes the volatility of the cash flows of the first period is preferred[36] (see below in Corporate Finance for an explanation related to the estimation of the NPV and the volatility of the project).
Limitations
La relevancia de las opciones reales, incluso como marco mental, puede verse limitada debido a consideraciones de mercado, organizativas o técnicas.[48] Cuando se emplea el marco, por lo tanto, el analista debe considerar previamente lo siguiente para determinar si la ROV es relevante para el proyecto en cuestión.
Market characteristics
As already explained, the market and environment underlying the project must be those in which "change is most evident", and the "source, trends and evolution" in the supply and demand of the product create the "flexibility, contingency and volatility"[31] that result in optionality. In other cases it is better to use the VAN method.
Organizational considerations
Real options are "particularly important for companies with some key characteristics",[31] and may be less relevant in other cases.[36] In summary, it is important to consider the following in determining whether the ROV framework is applicable:.
The corporate strategy has to adapt to contingent events. Some corporations face organizational rigidities and cannot react to market changes; In this case, the NPV approach is more appropriate.
In practice, the company must be positioned in such a way that it has an adequate flow of information and opportunities to act. Often this will be a market leader or a company that enjoys economies of scale and scope.
Management must understand options, be able to identify and create them, and exercise them appropriately.[16] This contrasts with business leaders focused on maintaining the status quo or short-term accounting profits.
The financial position of the company must be such that it has the ability to finance the project when necessary (i.e., issue shares, take on more debt or use internally generated cash flow). Management must, therefore, have appropriate access to this capital.
Management must be able to exercise real options. Some may be exercised by a single party, while others may require the agreement of several.
Technical considerations
Limitations in the use of these models arise due to the contrast between real options and financial options, for which these models were originally developed. The main difference is that the underlying is often not tradable on a stock market – for example, the owner of the factory cannot sell it easily and quickly, as he can with a stock. Furthermore, the real option itself may also not be (in this stock market sense) negotiable – for example, the factory owner cannot sell the right to expand his factory to another party; only he can make this decision. However, some real options can be sold. For example, ownership of vacant land is a real option to develop it in the future. Even where a market exists – for the underlying or for the option – in most cases market liquidity is limited (or non-existent). Finally, even if the company can actively adapt to market changes, the correct paradigm for discounting future claims remains to be determined.
The difficulties are then:
As noted above, data issues arise regarding the estimation of key inputs to the model. In this case, since the value or price of the underlying cannot be observed (directly), there will always be uncertainty as to its value and volatility (in turn increased by uncertainty as to possible management actions in the future).
It is often difficult to grasp the rules for the exercise of each of the real options and the consequent actions by management. Furthermore, a project may have a broad set of real options, some of which may be mutually exclusive.[16].
Theoretical difficulties may also arise, which are more serious.
These problems are addressed through several interrelated assumptions:
As explained above, data problems are usually addressed through a simulation of the project or a proxy listed on some stock exchange. Several new methods—such as those described above—also address these issues.
Likewise, as noted above, specific exercise rules can often be accommodated by encoding them in a custom binomial tree.[49].
Theoretical problems:
History
Although business managers have made capital investment decisions for centuries, the term "real option" is relatively new and was coined by Professor Stewart Myers of the MIT Sloan School of Management in 1977. In 1930, Irving Fisher wrote explicitly about the "options" available to the owner of a business (The Theory of Interest, II. viii). However, the description of such opportunities as "real options" followed the development of analytical techniques (such as the Black-Scholes Model in 1973) for financial options. For this reason the term "real option" is closely linked to these techniques.
Real options are today an active field of academic research. Professor Lenos Trigeorgis has been a prominent name for many years and has published several influential academic books and articles. Other pioneering scholars in the field include Professors Michael Brennan, Eduardo Schwartz, Graham Davis, Gonzalo Cortazar, Han Smit, Avinash Dixit, and Robert Pindyck (the latter two authors of the pioneering text in the discipline). An academic conference on real options is organized annually (Annual International Conference on Real Options).
Among others, the concept was popularized by Michael J. Mauboussin, then chief US investment strategist for Credit Suisse First Boston.[31] He uses real options to explain the gap between how the stock market values some companies and the "intrinsic value (finance)" of those companies. Trigeorgis has also disseminated real options through articles (for laymen) in publications such as The Wall Street Journal.[29] This popularization is such that ROV is now a standard offering in graduate finance degrees and often even in MBA curricula at many business schools.
Recently, real options have been used in business strategy, both for valuation purposes and as a conceptual framework.[13][14] The idea of treating strategic investments as options was popularized by Timothy Luehrman[50] in two HBR articles:[24] "In financial terms, a business strategy is much more like a series of options than a series of static cash flows." Investment opportunities are plotted in an “option space” with dimensions of “volatility” and value-to-cost ratio (“NPVc”).
Luehrman also co-authored with William Teichner a Harvard Business School case study, Arundel Partners: The Sequel Project, in 1992, which may have been the first business school case study to teach ROV. Reflecting the "integration" of ROV, Professor Robert C. Merton discussed Arundel's essential points in the lecture he gave upon receiving the Nobel Prize in 1997.[52] Arundel involves a group of investors considering acquiring the rights to sequels to a portfolio of yet-to-be-released feature films. In particular, investors must determine the value of the rights to these sequels before any of the first films are produced. Here, investors are faced with 2 main options: they can produce an original film and a sequel at the same time or they can wait to decide on a sequel after the original film is released. The second approach, Merton says, provides the option of not shooting the sequel in the event that the initial film is not successful. This real option has economic value and can be valued monetarily using an option pricing model.
• - Kodukula, P., & Papudesu, C. (2006). Project valuation using real options: a practitioner's guide. J. Ross Publishing. ISBN 978-1932159431.
Applications:.
• - Grenadier, Steven R. & Weiss, Allen M., 1997. "Investment in technological innovations: An option pricing approach," Journal of Financial Economics, Elsevier, vol. 44(3), pages 397–416, June.
• - The Impact of Real Options in Agency Problems G. Siller-Pagaza, G. Otalora, E. Cobas-Flores (2006).
General
Theory
• - Introduction to real options valuation as a modeling problem Archived November 15, 2012 at the Wayback Machine., Mikael Collan.
• - The promise and peril of real options, Prof. Aswath Damodaran, Stern School of Business.
• - Real Options Tutorial, Prof. Marco Dias, PUC-Rio.
• - Valuation of real options: frequent errors, Prof. Pablo Fernández, IESE Business School, University of Navarra.
• - Identifying real options, Prof. Campbell R. Harvey. Duke University, Fuqua School of Business.
• - An introduction to real options Archived May 25, 2012 at the Wayback Machine. (Southern African Society of Investment Analysts), Prof. E. Gilbert, University of Cape Town.
• - Decision making under uncertainty: real options to the rescue?, Prof. Lucas Miller and Chan Park, Auburn University.
• - Real Options White Papers and Case Studies Archived February 8, 2012 at the Wayback Machine., Dr. Jonathan Mun.
• - Real options – Introduction, Portfolio Group.
• - How do you evaluate the value of a company's "real options"? Archived October 20, 2019 at the Wayback Machine., Prof. Alfred Rappaport Columbia University and Michael Mauboussin.
• - Some important issues involving real options: an overview, Gordon Sick and Andrea Gamba (2005).
• - Real Power of Real Options, Leslie and Michaels (1997), Keith Leslie and Max Michaels McKinsey Quarterly, 1997 (3) pages 4–22. Quoted by Robert Merton in his Nobel Prize acceptance speech in 1997. McKinsey Classic - Reprinted in McKinsey Anthology 2000 - On Strategy. Quoted in McKinsey Anthology 2011 - Have you tested your strategy lately?
Magazines
• - Real Options Magazine.
• - Magazine of Real Options and Strategy.
Calculation resources
• - ROV Spreadsheet Models, Prof. Aswath Damodaran, Stern School of Business.
• - Real Options Calculator, Prof. Steven T. Hackman, Georgia Institute of Technology.
[3] ↑ a b c Locatelli, Giorgio; Mancini, Mauro; Lotti, Giovanni (15 de abril de 2020). «A simple-to-implement real options method for the energy sector». Energy (en inglés) 197: 117226. ISSN 0360-5442. doi:10.1016/j.energy.2020.117226. Archivado desde el original el 4 de mayo de 2020.: http://eprints.whiterose.ac.uk/157998/
[6] ↑ Locatelli, Giorgio; Boarin, Sara; Pellegrino, Francesco; Ricotti, Marco E. (1 de febrero de 2015). «Load following with Small Modular Reactors (SMR): A real options analysis». Energy 80: 41-54. doi:10.1016/j.energy.2014.11.040.: http://eprints.whiterose.ac.uk/91139/1/Accpeted%20version.pdf
[9] ↑ Huang, Hsini; Jong, Simcha (2019). «Public Funding for Science and the Value of Corporate R&D Projects; Evidence from Project Initiation and Termination Decisions in Cell Therapy». Journal of Management Studies (en inglés) 56 (5): 1000-1039. ISSN 1467-6486. doi:10.1111/joms.12423.: https://es.wikipedia.org//portal.issn.org/resource/issn/1467-6486
[10] ↑ Gunther McGrath, Rita; Nerkar, Atul (January 2004). «Real options reasoning and a new look at the R&D investment strategies of pharmaceutical firms». Strategic Management Journal (en inglés) 25 (1): 1-21. ISSN 0143-2095. doi:10.1002/smj.358.: https://archive.org/details/sim_strategic-management-journal_2004-01_25_1/page/n3
[11] ↑ Yaish, Aviv; Zohar, Aviv (18 de junio de 2020). Pricing ASICs for Cryptocurrency Mining. arXiv:2002.11064.: http://arxiv.org/abs/2002.11064
[12] ↑ See Bilkic et al. under Real options valuation-Applications]].
[16] ↑ a b c Zhang, S.X.; Babovic, V. (2011). «An evolutionary real options framework for the design and management of projects and systems with complex real options and exercising conditions». Decision Support Systems 51 (1): 119-129. doi:10.1016/j.dss.2010.12.001.: https://www.researchgate.net/publication/220197192
[17] ↑ Real Academia Española. «real». Diccionario de la lengua española (23.ª edición).: https://dle.rae.es/real
[21] ↑ Lai, Chun Sing; Locatelli, Giorgio (February 2021). «Valuing the option to prototype: A case study with Generation Integrated Energy Storage». Energy 217: 119290. doi:10.1016/j.energy.2020.119290.: https://dx.doi.org/10.1016%2Fj.energy.2020.119290
[24] ↑ a b c d Timothy Luehrman: "Investment Opportunities as Real Options: Getting Started on the Numbers". Harvard Business Review 76, no. 4 (July – August 1998): 51–67.; "Strategy as a Portfolio of Real Options". Harvard Business Review 76, no. 5 (September–October 1998): 87-99.
[25] ↑ Ver: §32 "Certainty Equivalent Approach" & §165 "Risk Adjusted Discount Rate" in: Joel G. Siegel; Jae K. Shim; Stephen Hartman (1 de noviembre de 1997). Schaum's quick guide to business formulas: 201 decision-making tools for business, finance, and accounting students. McGraw-Hill Professional. ISBN 978-0-07-058031-2. Consultado el 12 de noviembre de 2011.: https://archive.org/details/schaumsquickguid00sieg
[32] ↑ Tan, Jackson J.; Trinidad, Fernando L. (15 de febrero de 2018). «A real options model for loan portfolios of actively traded Philippine universal banks». Journal of Global Entrepreneurship Research 8: 4. ISSN 2251-7316. doi:10.1186/s40497-018-0091-9.: https://es.wikipedia.org//portal.issn.org/resource/issn/2251-7316
[35] ↑ a b c Jenifer Piesse and Alexander Van de Putte. (2004). "Volatility estimation in Real Options". 8th Annual International Conference on Real Options.: http://www.financialcertified.com/article12.pdf
[41] ↑ Ver pág. 26 en Marion A. Brach (2003). Real Options in Practice. Wiley. ISBN 0471445568.
[42] ↑ a b See Ch. 23, Sec. 5, in: Frank Reilly, Keith Brown (2011). "Investment Analysis and Portfolio Management" (10th Edition). South-Western College Pub. ISBN 0538482389.
[43] ↑ Cortazar, Gonzalo; Gravet, Miguel; Urzua, Jorge (2008). «The valuation of multidimensional American real options using the LSM simulation method». Computers & Operations Research 35: 113-129. doi:10.1016/j.cor.2006.02.016.: http://www.gonzalocortazar.com/CortazarGravetUrzua2008.pdf
[45] ↑ Datar, V.; Mathews, S. (2004). «European Real Options: An Intuitive Algorithm for the Black Scholes Formula». Journal of Applied Finance 14 (1).
[47] ↑ Collan, M.; Fullér, R.; Mezei, J. (2009). «Fuzzy Pay-Off Method for Real Option Valuation». Journal of Applied Mathematics and Decision Sciences 2009 (13601): 1-15. doi:10.1155/2009/238196.: https://dx.doi.org/10.1155%2F2009%2F238196
Some analysts replace volatility in the value of the project with the proxy of a quoted security "Value (finance)"), using its price volatility or, if there are financial options on this quoted security, the implied volatility of these financial options.[1]
Dividends generated by the underlying asset: As part of a project, the dividend equals any income that could be derived from the asset and paid to the owner. The dividend reduces the appreciation of the asset.
• - Features of the option:
Strike price: corresponds to any investment outlay (non-recoverable), generally the prospective costs of the project. Generally, management would go ahead with the project if the present value of the expected cash flows exceeds this amount;
Option term: the time during which management can decide to act or not act corresponds to the life of the option. As noted above, examples include the time until a patent or mineral rights for a new mine expire. However, it should be considered that, given the flexibility related to time, this option term should be handled with caution.
Types of options and option exercise. Management's ability to respond to changes in value is modeled at each decision point as a series of options, which may include:
the option to contract the project (an American-style put option, put);
the option to leave the project (also a put option);
the option to expand the project (purchase option, call);
switching options or compound options.
Similarly, commonly used valuation methods are adapted from the valuation of financial options.[39][40] However, while most "real" problems allow for the American-style exercise at any point (many points) in the life of the project, and these problems are affected by multiple underlying variables, standard methods are limited either by dimensionality, or by the principles of the exercise, or even both.
When selecting a model, therefore, analysts must make a trade-off between these considerations. The model must also be flexible enough to allow the relevant decision rule to be appropriately encoded for each decision point.
• - Sometimes closed-form solutions "Closed Form (Mathematics)"), such as Black-Scholes, are used.[36] These are applicable only for European-style options or American perpetual options. It should be noted that this application of Black-Scholes assumes constant, that is, deterministic, costs; In cases where project costs are assumed to be stochastic, then, instead of Black-Scholes, the Margrabe formula should be applied,[41][42] assessing the possibility of "exchanging" expenses for income. Similarly, when the project is exposed to 2 (or more) uncertainties – for example, for natural resources, price and quantity – some analysts attempt to use an overall volatility, although this is more correctly treated as a rainbow option,[36] which is typically valued by simulation, as shown below.
• - The most used methods are binomial lattices.[31][40] These are most used, because most of the real options are American style. Furthermore, and in particular, models based on lattices (lattices) allow flexibility in terms of the exercise, because different relevant rules can be encoded in each node.[34] It should be considered that these lattices cannot easily handle problems with a high number of dimensions. Treating project costs as stochastic would add (at least) one dimension to the network, squaring the number of end nodes (the exponent here, corresponding to the number of sources of uncertainty).
• - Specialized Monte Carlo methods have also been developed and are increasingly applied, and especially, to high-dimensional problems. Note that for American-style real options, this application is somewhat more complex, although recent research[43] combines a least squares approach with simulation, allowing the valuation of real options that are both multidimensional and American-style.
• - When the real option can be modeled using a partial differential equation, the finite difference method is sometimes applied for the valuation of real options. Although many early ROV articles discussed this method,[44] its use is relatively uncommon today, particularly among professionals, due to the mathematical sophistication required. Nor can it be easily used for problems with a high number of dimensions.
Several other methods have been developed for the valuation of real options, aimed primarily at professionals.[3] They generally use cash flow scenarios for the projection of the future distribution of payments, and are not based on restrictive assumptions such as those underlying the closed-form (or even numerical) solutions already explained. More recent additions include the Datar-Mathews method,[45][46] the fuzzy payment method[47] and simulation with the optimized exercise thresholds method[3].
Some analysts replace volatility in the value of the project with the proxy of a quoted security "Value (finance)"), using its price volatility or, if there are financial options on this quoted security, the implied volatility of these financial options.[1]
Dividends generated by the underlying asset: As part of a project, the dividend equals any income that could be derived from the asset and paid to the owner. The dividend reduces the appreciation of the asset.
• - Features of the option:
Strike price: corresponds to any investment outlay (non-recoverable), generally the prospective costs of the project. Generally, management would go ahead with the project if the present value of the expected cash flows exceeds this amount;
Option term: the time during which management can decide to act or not act corresponds to the life of the option. As noted above, examples include the time until a patent or mineral rights for a new mine expire. However, it should be considered that, given the flexibility related to time, this option term should be handled with caution.
Types of options and option exercise. Management's ability to respond to changes in value is modeled at each decision point as a series of options, which may include:
the option to contract the project (an American-style put option, put);
the option to leave the project (also a put option);
the option to expand the project (purchase option, call);
switching options or compound options.
Similarly, commonly used valuation methods are adapted from the valuation of financial options.[39][40] However, while most "real" problems allow for the American-style exercise at any point (many points) in the life of the project, and these problems are affected by multiple underlying variables, standard methods are limited either by dimensionality, or by the principles of the exercise, or even both.
When selecting a model, therefore, analysts must make a trade-off between these considerations. The model must also be flexible enough to allow the relevant decision rule to be appropriately encoded for each decision point.
• - Sometimes closed-form solutions "Closed Form (Mathematics)"), such as Black-Scholes, are used.[36] These are applicable only for European-style options or American perpetual options. It should be noted that this application of Black-Scholes assumes constant, that is, deterministic, costs; In cases where project costs are assumed to be stochastic, then, instead of Black-Scholes, the Margrabe formula should be applied,[41][42] assessing the possibility of "exchanging" expenses for income. Similarly, when the project is exposed to 2 (or more) uncertainties – for example, for natural resources, price and quantity – some analysts attempt to use an overall volatility, although this is more correctly treated as a rainbow option,[36] which is typically valued by simulation, as shown below.
• - The most used methods are binomial lattices.[31][40] These are most used, because most of the real options are American style. Furthermore, and in particular, models based on lattices (lattices) allow flexibility in terms of the exercise, because different relevant rules can be encoded in each node.[34] It should be considered that these lattices cannot easily handle problems with a high number of dimensions. Treating project costs as stochastic would add (at least) one dimension to the network, squaring the number of end nodes (the exponent here, corresponding to the number of sources of uncertainty).
• - Specialized Monte Carlo methods have also been developed and are increasingly applied, and especially, to high-dimensional problems. Note that for American-style real options, this application is somewhat more complex, although recent research[43] combines a least squares approach with simulation, allowing the valuation of real options that are both multidimensional and American-style.
• - When the real option can be modeled using a partial differential equation, the finite difference method is sometimes applied for the valuation of real options. Although many early ROV articles discussed this method,[44] its use is relatively uncommon today, particularly among professionals, due to the mathematical sophistication required. Nor can it be easily used for problems with a high number of dimensions.
Several other methods have been developed for the valuation of real options, aimed primarily at professionals.[3] They generally use cash flow scenarios for the projection of the future distribution of payments, and are not based on restrictive assumptions such as those underlying the closed-form (or even numerical) solutions already explained. More recent additions include the Datar-Mathews method,[45][46] the fuzzy payment method[47] and simulation with the optimized exercise thresholds method[3].