Оценка реальных опционов

Реальная оценка вариантов , также часто называют анализ реальных опционов , ^[1] ( ROV или ROA ) применяется вариант методов оценки для бюджетирования капиталовложений решений. ^[2] реальный вариант сам по себе, является правом , но не обязательство, предпринять определенные бизнес - инициативы, такие как отсрочка, отказ, расширение, постановка, или заключать контракт инвестиционный проект. ^[3] Например, оценка реальных опционов может изучить возможность инвестирования в расширение завода фирмы и альтернативный вариант продажи завода. ^[4]

Реальные опционы обычно отличаются от обычных финансовых опционов тем, что они обычно не торгуются как ценные бумаги и обычно не предполагают принятия решений по базовому активу, который торгуется как финансовая ценная бумага. ^[5] Еще одно различие заключается в том, что здесь держатели опционов, то есть руководство, могут напрямую влиять на стоимость основного проекта опциона ; тогда как это не является соображением в отношении базовой безопасности финансового опциона. Более того, руководство не может измерить неопределенность с точки зрения волатильности., и вместо этого должны полагаться на свое восприятие неопределенности. В отличие от финансовых вариантов, руководство также должно создавать или открывать реальные варианты, и такой процесс создания и обнаружения включает в себя предпринимательскую или бизнес-задачу. Реальные опционы наиболее ценны при высокой неопределенности; Руководство обладает значительной гибкостью, чтобы изменить ход проекта в благоприятном направлении, и готово использовать имеющиеся возможности. ^[6]

Анализ реальных опционов, как дисциплина, простирается от его применения в корпоративных финансах до принятия решений в условиях неопределенности в целом, адаптируя методы, разработанные для финансовых опционов, к «реальным» решениям. Например, менеджеры НИОКР могут использовать оценку реальных опционов, чтобы помочь им справиться с различными неопределенностями при принятии решений о распределении ресурсов между проектами НИОКР. ^{[7] [8] [9] [10]} Примером, не связанным с бизнесом, может быть решение присоединиться к рабочей силе или, скорее, отказаться от нескольких лет дохода, чтобы учиться в аспирантуре . ^[11] Это, таким образом, вынуждает лиц, принимающих решения, четко выражать предположения, лежащие в основе их прогнозов, и по этой причине ROV все чаще используется в качестве инструмента при формулировании бизнес-стратегии . ^{[12] [13]} Такое расширение реальных опций на реальные проекты часто требует настраиваемых систем поддержки принятия решений , потому что в противном случае сложные составные реальные варианты станут слишком сложными для обработки. ^[14]

Типы реальных опционов [ править ]

Гибкость, доступная руководству, то есть фактические «реальные варианты», как правило, будет зависеть от размера проекта, сроков реализации проекта и его функционирования после того, как он будет установлен. ^[15] Во всех случаях любые (невозмещаемые) авансовые расходы, связанные с этой гибкостью, являются опционной премией . Реальные опционы также обычно применяются к оценке акций - см. Оценка бизнеса § Подходы к ценообразованию опционов - а также к различным другим «приложениям», упомянутым ниже .

Параметры, относящиеся к размеру проекта [ править ]

Если объем проекта не определен, гибкость в отношении размера соответствующих объектов имеет большое значение и представляет собой возможность выбора. ^[16]

• Возможность расширения : здесь проект построен с мощностью, превышающей ожидаемый уровень производства, чтобы при необходимости он мог производить с более высокими темпами. После этого у руководства есть возможность (но не обязанность) на расширение, т.е. исполнение опциона,  если условия окажутся благоприятными. Проект с возможностью расширения будет стоить дороже, поскольку избыток представляет собой опционную премию , но стоит больше, чем то же самое, без возможности расширения. Это эквивалент опциона колл .
• Возможность заключения контракта : проект спроектирован таким образом, что объем производства может быть сокращен в будущем, если условия окажутся неблагоприятными. Отказ от этих будущих расходов представляет собой исполнение опциона . Это эквивалент опциона пут , и опять же, избыточные авансовые расходы являются опционной премией .
• Возможность расширения или сжатия : здесь проект спроектирован таким образом, что его работу можно динамически включать и выключать. Руководство может закрыть часть или все операции при неблагоприятных условиях (опцион пут) и может возобновить операции при улучшении условий (опцион колл). Гибкая производственная система (ГПС) является хорошим примером этого типа опциона. Эта опция также известна как опция переключения .

Варианты, относящиеся к срокам и срокам проекта [ править ]

В случае неопределенности относительно того, когда и как возникнут деловые или другие условия, гибкость в отношении сроков реализации соответствующего проекта (ов) имеет значение и представляет собой возможность выбора. Варианты роста , пожалуй, самые общие в этой категории - они включают в себя возможность реализовывать только те проекты, которые кажутся прибыльными на момент запуска.

• Варианты инициирования или отсрочки : здесь руководство может выбирать, когда начинать проект. Например, при разведке природных ресурсов компания может отложить разработку месторождения до тех пор, пока рыночные условия не станут благоприятными. Это опцион колл в американском стиле .
• Возможность отсрочки с патентом на продукт : Фирма, имеющая патентное право на продукт, имеет право разрабатывать и продавать продукт исключительно до истечения срока действия патента. Фирма будет продавать и разрабатывать продукт только в том случае, если текущая стоимость ожидаемых денежных потоков от продажи продукта превышает затраты на разработку. Если этого не происходит, фирма может отложить патент и не нести никаких дополнительных расходов.
• Возможность отказаться : руководство может иметь возможность прекратить проект в течение его жизненного цикла и, возможно, реализовать его спасательную ценность . Здесь, когда текущая стоимость оставшихся денежных потоков падает ниже ликвидационной стоимости, актив может быть продан, и это действие фактически является исполнением пут-опциона . Этот вариант также известен как вариант завершения . Варианты отказа выполнены в американском стиле .
• Варианты последовательности: этот вариант связан с вариантом запуска, описанным выше, хотя влечет за собой гибкость в отношении сроков выполнения более чем одного взаимосвязанных проектов: анализ здесь заключается в том, выгодно ли реализовывать их последовательно или параллельно . Здесь, наблюдая за результатами, относящимися к первому проекту, фирма может разрешить некоторую неопределенность, связанную с предприятием в целом. После решения у руководства есть возможность продолжить или нет разработку других проектов. При параллельном подходе руководство уже израсходовало бы ресурсы, и ценность возможности не тратить их теряется. Последовательность проектов - важный аспект корпоративной стратегии.. С этим также связано понятие вариантов «Интрапроект» и «Интерпроект».
• Вариант прототипа : новые системы производства и хранения энергии постоянно разрабатываются из-за изменения климата, нехватки ресурсов и законов об окружающей среде. Некоторые системы представляют собой постепенные инновации существующих систем, а другие - радикальные инновации. Радикальные инновационные системы - это рискованные инвестиции из-за их технической и экономической неопределенности. Создание прототипов может застраховать эти риски, потратив часть стоимости полномасштабной системы и взамен получив экономическую и техническую информацию о системе. С экономической точки зрения создание прототипа - это вариант хеджирования рисков, связанных с затратами, которые необходимо должным образом оценить. ^[17]

Опции, относящиеся к работе проекта [ править ]

Руководство может иметь гибкость в отношении производимого продукта и / или процесса, используемого в производстве . Эта гибкость представляет собой необязательность.

• Варианты сочетания выходных данных : возможность получения различных выходных данных на одном предприятии называется вариантом сочетания выходных данных или гибкостью продукта . Эти варианты особенно ценны в отраслях, где спрос нестабилен или где общие объемы спроса на конкретный товар, как правило, низкие, и руководство хотело бы быстро перейти на другой продукт, если это необходимо.
• Варианты микширования входов : вариант смешивания входов - гибкость процесса  - позволяет руководству использовать разные входы для получения одинаковых выходных данных по мере необходимости. Например, фермер оценит возможность переключения между различными источниками кормов, предпочитая использовать наиболее дешевую приемлемую альтернативу. Например, электроэнергетическая компания может иметь возможность переключаться между различными источниками топлива для производства электроэнергии и, следовательно, гибкую установку, хотя более дорогая может быть более ценной.
• Варианты рабочего масштаба : руководство может иметь возможность изменить производительность за единицу времени или изменить общую продолжительность производственного цикла, например, в ответ на рыночные условия. Эти параметры также известны как параметры интенсивности .

Оценка [ править ]

С учетом вышеизложенного, очевидно , что существует аналогия между реальным опционам и финансовые возможности , ^[18] , и поэтому мы ожидаем , что варианты на основе моделирования и анализа для применения здесь. В то же время, тем не менее, важно понимать, почему более стандартные методы оценки могут быть неприменимы для ROV. ^[2]

Применимость стандартных методик [ править ]

ROV is often contrasted with more standard techniques of capital budgeting, such as discounted cash flow (DCF) analysis / net present value (NPV).^[2] Under this "standard" NPV approach, future expected cash flows are present valued under the empirical probability measure at a discount rate that reflects the embedded risk in the project; see CAPM, APT, WACC. Here, only the expected cash flows are considered, and the "flexibility" to alter corporate strategy in view of actual market realizations is "ignored"; see below as well as Corporate finance § Valuing flexibility. The NPV framework (implicitly) assumes that management is "passive" with regard to their Capital Investment once committed. Some analysts account for this uncertainty by (i) adjusting the discount rate, e.g. by increasing the cost of capital, or (ii) adjusting the cash flows, e.g. using certainty equivalents, or (iii) applying (subjective) "haircuts" to the forecast numbers, or (iv) via probability-weighting these as in rNPV.^[19][20][21] Even when employed, however, these latter methods do not normally properly account for changes in risk over the project's lifecycle and hence fail to appropriately adapt the risk adjustment.^[22][23]

By contrast, ROV assumes that management is "active" and can "continuously" respond to market changes. Real options consider "all" scenarios (or "states") and indicate the best corporate action in each of these contingent events.^[24] Because management adapts to each negative outcome by decreasing its exposure and to positive scenarios by scaling up, the firm benefits from uncertainty in the underlying market, achieving a lower variability of profits than under the commitment/NPV stance. The contingent nature of future profits in real option models is captured by employing the techniques developed for financial options in the literature on contingent claims analysis. Here the approach, known as risk-neutral valuation, consists in adjusting the probability distribution for risk consideration, while discounting at the risk-free rate. This technique is also known as the "martingale" approach, and uses a risk-neutral measure. For technical considerations here, see below.

Given these different treatments, the real options value of a project is typically higher than the NPV – and the difference will be most marked in projects with major flexibility, contingency, and volatility.^[25] As for financial options higher volatility of the underlying leads to higher value. (An application of Real Options Valuation in the Philippine banking industry exhibited that increased levels of income volatility may adversely affect option values on the loan portfolio, when the presence of information asymmetry is considered. In this case, increased volatility may limit the value of an option.^[26]) Part of the criticism (and subsequently slow adoption) of Real Options Valuation in practice and academe stems from the generally higher values for underlying assets these functions generate. However, studies have shown that these models are reliable estimators of underlying asset value, when input values are properly identified.^[27]

Options based valuation[edit]

Although there is much similarity between the modelling of real options and financial options,^[18][28] ROV is distinguished from the latter, in that it takes into account uncertainty about the future evolution of the parameters that determine the value of the project, coupled with management's ability to respond to the evolution of these parameters.^[29][30] It is the combined effect of these that makes ROV technically more challenging than its alternatives.

First, you must figure out the full range of possible values for the underlying asset.... This involves estimating what the asset's value would be if it existed today and forecasting to see the full set of possible future values... [These] calculations provide you with numbers for all the possible future values of the option at the various points where a decision is needed on whether to continue with the project...^[28]

When valuing the real option, the analyst must therefore consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply. Conceptually, valuing a real option looks at the premium between inflows and outlays for a particular project. Inputs to the value of a real option (time, discount rates, volatility, cash inflows and outflows) are each affected by the terms of business, and external environmental factors that a project exists in. Terms of business as information regarding ownership, data collection costs, and patents, are formed in relation to political, environmental, socio-cultural, technological, environmental and legal factors that affect an industry. Just as terms of business are affected by external environmental factors, these same circumstances affect the volatility of returns, as well as the discount rate (as firm or project specific risk). Furthermore, the external environmental influences that affect an industry affect projections on expected inflows and outlays.^[31]

Valuation inputs[edit]

Given the similarity in valuation approach, the inputs required for modelling the real option correspond, generically, to those required for a financial option valuation.^[18][28][29] The specific application, though, is as follows:

• The option's underlying is the project in question – it is modelled in terms of:
  • Spot price: the starting or current value of the project is required: this is usually based on management's "best guess" as to the gross value of the project's cash flows and resultant NPV;
  • Volatility: a measure for uncertainty as to the change in value over time is required:
    • the volatility in project value is generally used, usually derived via monte carlo simulation;^[29][32] sometimes the volatility of the first period's cash flows are preferred;^[30] see further under Corporate finance for a discussion relating to the estimation of NPV and project volatility.
    • some analysts substitute a listed security as a proxy, using either its price volatility (historical volatility), or, if options exist on this security, their implied volatility.^[1]
  • Dividends generated by the underlying asset: As part of a project, the dividend equates to any income which could be derived from real assets and paid to the owner. These reduce the appreciation of the asset.
• Option characteristics:
  • Strike price: this corresponds to any (non-recoverable) investment outlays, typically the prospective costs of the project. In general, management would proceed (i.e. the option would be in the money) given that the present value of expected cash flows exceeds this amount;
  • Option term: the time during which management may decide to act, or not act, corresponds to the life of the option. As above, examples include the time to expiry of a patent, or of the mineral rights for a new mine. See Option time value. Note though that given the flexibility related to timing as described, caution must be applied here.
  • Option style and option exercise. Management's ability to respond to changes in value is modeled at each decision point as a series of options, as above these may comprise, i.a.:
    • the option to contract the project (an American styled put option);
    • the option to abandon the project (also an American put);
    • the option to expand or extend the project (both American styled call options);
    • switching options or composite options which may also apply to the project.

Valuation methods[edit]

The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options.^[33][34] Note though that, in general, while most "real" problems allow for American style exercise at any point (many points) in the project's life and are impacted by multiple underlying variables, the standard methods are limited either with regard to dimensionality, to early exercise, or to both. In selecting a model, therefore, analysts must make a trade off between these considerations; see Option (finance) § Model implementation. The model must also be flexible enough to allow for the relevant decision rule to be coded appropriately at each decision point.

• Closed form, Black–Scholes-like solutions are sometimes employed.^[30] These are applicable only for European styled options or perpetual American options. Note that this application of Black–Scholes assumes constant — i.e. deterministic — costs: in cases where the project's costs, like its revenue, are also assumed stochastic, then Margrabe's formula can (should) be applied instead,^[35][36] here valuing the option to "exchange" expenses for revenue. (Relatedly, where the project is exposed to two (or more) uncertainties — e.g. for natural resources, price and quantity — some analysts attempt to use an overall volatility; this, though, is more correctly treated as a rainbow option,^[30] typically valued using simulation as below.)
• The most commonly employed methods are binomial lattices.^[25][34] These are more widely used given that most real options are American styled. Additionally, and particularly, lattice-based models allow for flexibility as to exercise, where the relevant, and differing, rules may be encoded at each node.^[28] Note that lattices cannot readily handle high-dimensional problems; treating the project's costs as stochastic would add (at least) one dimension to the lattice, increasing the number of ending-nodes by the square (the exponent here, corresponding to the number of sources of uncertainty).
• Specialised Monte Carlo Methods have also been developed and are increasingly, and especially, applied to high-dimensional problems.^[37] Note that for American styled real options, this application is somewhat more complex; although recent research^[38] combines a least squares approach with simulation, allowing for the valuation of real options which are both multidimensional and American styled; see Monte Carlo methods for option pricing § Least Square Monte Carlo.
• When the Real Option can be modelled using a partial differential equation, then Finite difference methods for option pricing are sometimes applied. Although many of the early ROV articles discussed this method,^[39] its use is relatively uncommon today—particularly amongst practitioners—due to the required mathematical sophistication; these too cannot readily be used for high-dimensional problems.

Various other methods, aimed mainly at practitioners, have been developed for real option valuation.^[3] These typically use cash-flow scenarios for the projection of the future pay-off distribution, and are not based on restricting assumptions similar to those that underlie the closed form (or even numeric) solutions discussed. The most recent additions include the Datar–Mathews method,^[40][41] fuzzy pay-off method,^[42] the simulation with optimised exercise thresholds method.^[3]

Limitations[edit]

The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations.^[43] When the framework is employed, therefore, the analyst must first ensure that ROV is relevant to the project in question. These considerations are as follows.

Market characteristics[edit]

As discussed above, the market and environment underlying the project must be one where "change is most evident", and the "source, trends and evolution" in product demand and supply, create the "flexibility, contingency, and volatility" ^[25]which result in optionality. Without this, the NPV framework would be more relevant.

Organizational considerations[edit]

Real options are "particularly important for businesses with a few key characteristics",^[25] and may be less relevant otherwise.^[30] In overview, it is important to consider the following in determining that the RO framework is applicable:

1. Corporate strategy has to be adaptive to contingent events. Some corporations face organizational rigidities and are unable to react to market changes; in this case, the NPV approach is appropriate.
2. Practically, the business must be positioned such that it has appropriate information flow, and opportunities to act. This will often be a market leader and / or a firm enjoying economies of scale and scope.
3. Management must understand options, be able to identify and create them, and appropriately exercise them.^[14] This contrasts with business leaders focused on maintaining the status quo and / or near-term accounting earnings.
4. The financial position of the business must be such that it has the ability to fund the project as, and when, required (i.e. issue shares, absorb further debt and / or use internally generated cash flow); see Financial statement analysis. Management must, correspondingly, have appropriate access to this capital.
5. Management must be in the position to exercise, in so far as some real options are proprietary (owned or exercisable by a single individual or a company) while others are shared (can (only) be exercised by many parties).

Technical considerations[edit]

Limitations as to the use of these models arise due to the contrast between Real Options and financial options, for which these were originally developed. The main difference is that the underlying is often not tradable – e.g. the factory owner cannot easily sell the factory upon which he has the option. Additionally, the real option itself may also not be tradeable – e.g. the factory owner cannot sell the right to extend his factory to another party, only he can make this decision (some real options, however, can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the future). Even where a market exists – for the underlying or for the option – in most cases there is limited (or no) market liquidity. Finally, even if the firm can actively adapt to market changes, it remains to determine the right paradigm to discount future claims

The difficulties, are then:

1. As above, data issues arise as far as estimating key model inputs. Here, since the value or price of the underlying cannot be (directly) observed, there will always be some (much) uncertainty as to its value (i.e. spot price) and volatility (further complicated by uncertainty as to management's actions in the future).
2. It is often difficult to capture the rules relating to exercise, and consequent actions by management. Further, a project may have a portfolio of embedded real options, some of which may be mutually exclusive.^[14]
3. Theoretical difficulties, which are more serious, may also arise.^[44]

• Option pricing models are built on rational pricing logic. Here, essentially: (a) it is presupposed that one can create a "hedged portfolio" comprising one option and "delta" shares of the underlying. (b) Arbitrage arguments then allow for the option's price to be estimated today; see Rational pricing § Delta hedging. (c) When hedging of this sort is possible, since delta hedging and risk neutral pricing are mathematically identical, then risk neutral valuation may be applied, as is the case with most option pricing models. (d) Under ROV however, the option and (usually) its underlying are clearly not traded, and forming a hedging portfolio would be difficult, if not impossible.
• Standard option models: (a) Assume that the risk characteristics of the underlying do not change over the life of the option, usually expressed via a constant volatility assumption. (b) Hence a standard, risk free rate may be applied as the discount rate at each decision point, allowing for risk neutral valuation. Under ROV, however: (a) managements' actions actually change the risk characteristics of the project in question, and hence (b) the Required rate of return could differ depending on what state was realised, and a premium over risk free would be required, invalidating (technically) the risk neutrality assumption.

These issues are addressed via several interrelated assumptions:

1. As discussed above, the data issues are usually addressed using a simulation of the project, or a listed proxy. Various new methods – see for example those described above – also address these issues.
2. Also as above, specific exercise rules can often be accommodated by coding these in a bespoke binomial tree; see:.^[28]
3. The theoretical issues:

• To use standard option pricing models here, despite the difficulties relating to rational pricing, practitioners adopt the "fiction" that the real option and the underlying project are both traded: the so called, Marketed Asset Disclaimer (MAD) approach. Although this is a strong assumption, it is pointed out that a similar fiction in fact underpins standard NPV / DCF valuation (and using simulation as above). See:^[1] and.^[28]
• To address the fact that changing characteristics invalidate the use of a constant discount rate, some analysts use the "replicating portfolio approach", as opposed to Risk neutral valuation, and modify their models correspondingly.^[28][36] Under this approach, (a) we "replicate" the cash flows on the option by holding a risk free bond and the underlying in the correct proportions. Then, (b) since the cash flows of the option and the portfolio will always be identical, by arbitrage arguments their values may (must) be equated today, and (c) no discounting is required.

History[edit]

Whereas business managers have been making 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 of the "options" available to a business owner (The Theory of Interest, II.VIII). The description of such opportunities as "real options", however, followed on the development of analytical techniques for financial options, such as Black–Scholes in 1973. As such, the term "real option" is closely tied to these option methods.

Real options are today an active field of academic research. Professor Lenos Trigeorgis has been a leading name for many years, publishing several influential books and academic articles. Other pioneering academics in the field include Professors Michael Brennan, Eduardo Schwartz, Graham Davis, Gonzalo Cortazar, Han Smit, Avinash Dixit and Robert Pindyck (the latter two, authoring the pioneering text in the discipline). An academic conference on real options is organized yearly (Annual International Conference on Real Options).

Amongst others, the concept was "popularized" by Michael J. Mauboussin, then chief U.S. investment strategist for Credit Suisse First Boston.^[25] He uses real options to explain the gap between how the stock market prices some businesses and the "intrinsic value" for those businesses. Trigeorgis also has broadened exposure to real options through layman articles in publications such as The Wall Street Journal.^[24] This popularization is such that ROV is now a standard offering in postgraduate finance degrees, and often, even in MBA curricula at many Business Schools.

Recently, real options have been employed in business strategy, both for valuation purposes and as a conceptual framework.^[12][13] The idea of treating strategic investments as options was popularized by Timothy Luehrman ^[45] in two HBR articles:^[18] "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 "volatility" & value-to-cost ("NPVq").

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.^[46] Reflecting the "mainstreaming" of ROV, Professor Robert C. Merton discussed the essential points of Arundel in his Nobel Prize Lecture in 1997.^[47] Arundel involves a group of investors that is considering acquiring the sequel rights to a portfolio of yet-to-be released feature films. In particular, the investors must determine the value of the sequel rights before any of the first films are produced. Here, the investors face two main choices. They can produce an original movie and sequel at the same time or they can wait to decide on a sequel after the original film is released. The second approach, he states, provides the option not to make a sequel in the event the original movie is not successful. This real option has economic worth and can be valued monetarily using an option-pricing model. See Option (filmmaking).

See also[edit]

• Option contract
• Opportunity cost
• Monte Carlo methods in finance
• Contingent claim valuation
• Fuzzy pay-off method for real option valuation
• Datar–Mathews method for real option valuation
• Business valuation § Option pricing approaches
• Corporate finance § Valuing flexibility
• Government procurement in the United States § Real options analysis
• Principal–agent problem § Options framework
• Patent valuation § Option-based method
• Contingent value rights

References[edit]

Further reading[edit]

Standard texts:

• Amram, Martha; Kulatilaka,Nalin (1999). Real Options: Managing Strategic Investment in an Uncertain World. Boston: Harvard Business School Press. ISBN 978-0-87584-845-7.
• Brach, Marion A. (2003). Real Options in Practice. New York: Wiley. ISBN 978-0471445562.
• Copeland, Thomas E.; Vladimir Antikarov (2001). Real Options: A Practitioner's Guide. New York: Texere. ISBN 978-1-58799-028-1.
• Dixit, A.; R. Pindyck (1994). Investment Under Uncertainty. Princeton: Princeton University Press. ISBN 978-0-691-03410-2.
• Moore, William T. (2001). Real Options and Option-embedded Securities. New York: John Wiley & Sons. ISBN 978-0-471-21659-9.
• Müller, Jürgen (2000). Real Option Valuation in Service Industries. Wiesbaden: Deutscher Universitäts-Verlag. ISBN 978-3-8244-7138-6.
• Smit, T.J.; Trigeorgis, Lenos (2004). Strategic Investment: Real Options and Games. Princeton: Princeton University Press. ISBN 978-0-691-01039-7.
• Trigeorgis, Lenos (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge: The MIT Press. ISBN 978-0-262-20102-5.

Applications:

• Brennan, Michael J.; Schwartz, Eduardo S. (1985). "Evaluating Natural Resource Investments". The Journal of Business. 58 (2): 135–157. doi:10.1086/296288. JSTOR 2352967.
• Aswath Damodaran. "Applications of option pricing theory to equity valuation". Cite journal requires |journal= (help)
• Daryl G. Waldron. "Valuing Alternative Market Entry Strategies as "Real-Options"" (PDF). Cite journal requires |journal= (help)
• Richard de Neufville. "Real options in public infrastructures". Cite journal requires |journal= (help)
• Don Chance; Eric Hillebrand; Jimmy Hilliard (June 2009). "Pricing options on film revenue". Risk.net.
• S. Young; J. Gong; W. Van der Stede (2012). "Using real options to make decisions in the motion picture industry". LSE.
• David Lackner. "Strategic Technology Investment Decisions in Research & Development". Cite journal requires |journal= (help)
• Heikkilä, Markku; Collan, Mikael (September 2011). "Enhancing Patent Valuation". Journal of Intellectual Property Rights. 16 (5).
• Sidak, J. Gregory; Leonard, Gregory K.; Hausman, Jerry A. (2007). "Patent Damages and Real Options: How Judicial Characterization of Non-Infringing Alternatives Reduces Incentives to Innovate". SSRN 931014. Cite journal requires |journal= (help)
• Fernando Torres (2006-09-11). "Establishing Licensing Rates Through Options". SSRN 1014743. Cite journal requires |journal= (help)
• Ehud Ronn, Valery Kholodnyi, Shannon Burchett. "Real Options and Energy Management". Cite journal requires |journal= (help)CS1 maint: multiple names: authors list (link)
• D. Mauer; S. Sarkar (2001). "Real Options, Agency Conflicts, and Financial Policy" (PDF). Archived from the original (PDF) on 2016-03-04.
• The Impact of Real Options in Agency Problems G. Siller-Pagaza, G. Otalora, E. Cobas-Flores (2006).
• Natasa Bilkic, Thomas Gries and Margarethe Pilichowski. (October 2012). "Stay in School or Start Working? - The Human Capital Investment Decision under Uncertainty and Irreversibility" (PDF). Labour Economics. 19 (5): 706–717. doi:10.1016/j.labeco.2012.04.005. S2CID 154917586.
• Karpoff, Jonathan M. (1989). "Characteristics of Limited Entry Fisheries and the Option Component of Entry Licenses". Land Economics. 65 (4): 386–393. doi:10.2307/3146806. JSTOR 3146806.

External links[edit]

Theory[edit]

• Intro to Real Option Valuation as a Modelling Problem, Mikael Collan
• The Promise and Peril of Real Options, Prof. Aswath Damodaran, Stern School of Business
• Real Options Tutorial, Prof. Marco Dias, PUC-Rio
• Valuing Real Options: Frequently Made Errors, Prof. Pablo Fernandez, IESE Business School, University of Navarra
• Identifying real options, Prof. Campbell R. Harvey. Duke University, Fuqua School of Business
• An introduction to real options (Investment Analysts Society of Southern Africa), Prof E. Gilbert, University of Cape Town
• Decision Making Under Uncertainty—Real Options to the Rescue?, Prof. Luke Miller & Chan Park, Auburn University
• Real Options Whitepapers and Case-studies, Dr. Jonathan Mun
• Real Options – Introduction, Portfolion Group
• How Do You Assess The Value of A Company's "Real Options"?, 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. Cited by Robert Merton in his Nobel Prize Acceptance Speech in 1997. McKinsey classic - Reprinted in McKinsey Anthology 2000 - On Strategy. Cited in McKinsey Anthology 2011 - Have You Tested Your Strategy Lately.

Journals[edit]

• Journal of Real Options
• Journal of Real Options and Strategy

Calculation resources[edit]

• ROV Spreadsheet Models, Prof. Aswath Damodaran, Stern School of Business
• Real Options Calculator, Prof. Steven T. Hackman, Georgia Institute of Technology