Real options valuation

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Real options valuation, also often termed real options analysis, [1] (ROV or ROA) applies option valuation techniques to capital budgeting decisions. [2] A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real call or put option, respectively. [3]

Option (finance) Right to buy or sell a certain thing at a later date at an agreed price

In finance, an option is a contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price prior to or on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed.

In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see Mathematical finance #Derivatives pricing: the Q world for discussion of the mathematics, Financial engineering for the implementation, as well as Financial modeling #Quantitative finance generally.

Capital budgeting Planning process used to assess an organizations long term investments

Capital budgeting, and investment appraisal, is the planning process used to determine whether an organization's long term investments such as new machinery, replacement of machinery, new plants, new products, and research development projects are worth the funding of cash through the firm's capitalization structure. It is the process of allocating resources for major capital, or investment, expenditures. One of the primary goals of capital budgeting investments is to increase the value of the firm to the shareholders.

Contents

Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security. [4] A further distinction is that option holders here, i.e. management, can directly influence the value of the option's underlying project; whereas this is not a consideration as regards the underlying security of a financial option. Moreover, management cannot measure uncertainty in terms of volatility, and must instead rely on their perceptions of uncertainty. Unlike financial options, management also have to create or discover real options, and such creation and discovery process comprises an entrepreneurial or business task. Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction and is willing to exercise the options. [5]

In finance, the underlying of a derivative is an asset, basket of assets, index, or even another derivative, such that the cash flows of the (former) derivative depend on the value of this underlying. There must be an independent way to observe this value to avoid conflicts of interest.

Volatility (finance) degree of variation of a trading price series over time

In finance, volatility is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.

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 Valuation to help them allocate their R&D budget among diverse projects; a non business example might be the decision to join the work force, or rather, to forgo several years of income to attend graduate school. [6] It, thus, forces decision makers to be explicit about the assumptions underlying their projections, and for this reason ROV is increasingly employed as a tool in business strategy formulation. [7] [8] This extension of real options to real-world projects often requires customized decision support systems, because otherwise the complex compound real options will become too intractable to handle. [9]

Corporate finance area of finance dealing with the sources of funding and the capital structure of corporations

Corporate finance is an area of finance that deals with sources of funding, the capital structure of corporations, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value. Although it is in principle different from managerial finance which studies the financial management of all firms, rather than corporations alone, the main concepts in the study of corporate finance are applicable to the financial problems of all kinds of firms.

Graduate school school that awards advanced academic degrees (i.e. masters and doctoral degrees) with the general requirement that students must have earned a previous undergraduate (bachelors) degree

A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate (bachelor's) degree with a high grade point average. A distinction is typically made between graduate schools and professional schools, which offer specialized advanced degrees in professional fields such as medicine, nursing, business, engineering, speech-language pathology, or law. The distinction between graduate schools and professional schools is not absolute, as various professional schools offer graduate degrees and vice versa.

Decision support system computer-based information system that supports business or organizational decision-making

A decision support system (DSS) is an information system that supports business or organizational decision-making activities. DSSs serve the management, operations and planning levels of an organization and help people make decisions about problems that may be rapidly changing and not easily specified in advance—i.e. unstructured and semi-structured decision problems. Decision support systems can be either fully computerized or human-powered, or a combination of both.

Types of real option

Simple Examples
Investment

This simple example shows the relevance of the real option to delay investment and wait for further information, and is adapted from "Investment Example".Cite web requires |website= (help).

Consider a firm that has the option to invest in a new factory. It can invest this year or next year. The question is: when should the firm invest? If the firm invests this year, it has an income stream earlier. But, if it invests next year, the firm obtains further information about the state of the economy, which can prevent it from investing with losses.

The firm knows its discounted cash flows if it invests this year: 5M. If it invests next year, the discounted cash flows are 6M with a 66.7% probability, and 3M with a 33.3% probability. Assuming a risk neutral rate of 10%, future discounted cash flows are, in present terms, 5.45M and 2.73M, respectively. The investment cost is 4M. If the firm invests next year, the present value of the investment cost is 3.63M.

Following the net present value rule for investment, the firm should invest this year because the discounted cash flows (5M) are greater than the investment costs (4M) by 1M. Yet, if the firm waits for next year, it only invests if discounted cash flows do not decrease. If discounted cash flows decrease to 3M, then investment is no longer profitable. If, they grow to 6M, then the firm invests. This implies that the firm invests next year with a 66.7% probability and earns 5.45M - 3.63M if it does invest. Thus the value to invest next year is 1.21M. Given that the value to invest next year exceeds the value to invest this year, the firm should wait for further information to prevent losses. This simple example shows how the net present value may lead the firm to take unnecessary risk, which could be prevented by real options valuation.

Staged Investment
Staged investments are quite often in the pharmaceutical, mineral, and oil industries. In this example, it is studied a staged investment abroad in which a firm decides whether to open one or two stores in a foreign country. This is adapted from "Staged Investment Example".Cite web requires |website= (help).

The firm does not know how well its stores are accepted in a foreign country. If their stores have high demand, the discounted cash flows per store is 10M. If their stores have low demand, the discounted cash flows per store is 5M. Assuming that the probability of both events is 50%, the expected discounted cash flows per store is 7.5M. It is also known that if the store's demand is independent of the store: if one store has high demand, the other also has high demand. The risk neutral rate is 10%. The investment cost per store is 8M.

Should the firm invest in one store, two stores, or not invest? The net present value suggests the firm should not invest: the net present value is -0.5M per store. But is it the best alternative? Following real options valuation, it is not: the firm has the real option to open one store this year, wait a year to know its demand, and invest in the new store next year if demand is high.

By opening one store, the firm knows that the probability of high demand is 50%. The potential value gain to expand next year is thus 50%*(10M-8M)/1.1 = 0.91M. The value to open one store this year is 7.5M - 8M = -0.5. Thus the value of the real option to invest in one store, wait a year, and invest next year is 0.41M. Given this, the firm should opt by opening one store. This simple example shows that a negative net present value does not imply that the firm should not invest.

The flexibility available to management – i.e. the actual "real options" – generically, will relate to project size, project timing, and the operation of the project once established. [10] In all cases, any (non-recoverable) upfront expenditure related to this flexibility is the option premium. Real options are also commonly applied to stock valuation - see Business valuation #Option pricing approaches - as well as to various other "Applications" referenced below.

Options relating to project size

Where the project's scope is uncertain, flexibility as to the size of the relevant facilities is valuable, and constitutes optionality. [11]

Options relating to project life and timing

Where there is uncertainty as to when, and how, business or other conditions will eventuate, flexibility as to the timing of the relevant project(s) is valuable, and constitutes optionality. Growth options are perhaps the most generic in this category – these entail the option to exercise only those projects that appear to be profitable at the time of initiation.

Options relating to project operation

Management may have flexibility relating to the product produced and /or the process used in manufacture. This flexibility constitutes optionality.

Valuation

Given the above, it is clear that there is an analogy between real options and financial options, [12] and we would therefore expect options-based modelling and analysis to be applied here. At the same time, it is nevertheless important to understand why the more standard valuation techniques may not be applicable for ROV. [2]

Applicability of standard techniques

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 adjusting the discount rate, e.g. by increasing the cost of capital, or the cash flows, e.g. using certainty equivalents, or applying (subjective) "haircuts" to the forecast numbers, or via probability-weighting as in rNPV. [13] [14] [15] 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. [16]

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. [17] 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 certainty-equivalent or 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. [18] 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. [19] ) 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. [20]

Options based valuation

Although there is much similarity between the modelling of real options and financial options, [12] [21] 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. [22] [23] It is the combined effect of these that makes ROV technically more challenging than its alternatives.

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. [24]

Valuation inputs

Given the similarity in valuation approach, the inputs required for modelling the real option correspond, generically, to those required for a financial option valuation. [12] [21] [22] The specific application, though, is as follows:

Valuation methods

The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options. [26] [27] 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. [23] 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, [28] [29] 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, [23] typically valued using simulation as below.)
  • The most commonly employed methods are binomial lattices. [18] [27] 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. [21] 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. [30] Note that for American styled real options, this application is somewhat more complex; although recent research [31] 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, [32] 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. 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 [33] [34] and the fuzzy pay-off method. [35]

Limitations

The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations. [36] When the framework is employed, therefore, the analyst must first ensure that ROV is relevant to the project in question. These considerations are as below.

Market characteristics

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" [18] which result in optionality. Without this, the NPV framework would be more relevant.

Organizational considerations

Real options are "particularly important for businesses with a few key characteristics", [18] and may be less relevant otherwise. [23] 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. [9] 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

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. [9]
  3. Theoretical difficulties, which are more serious, may also arise. [37]
  • 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:. [21]
  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. [21]
  • 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. [21] [29] 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

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 Eduardo Schwartz, Graham Davis, Gonzalo Cortazar, Michael Brennan, 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. [18] 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. [17] 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. [7] [8] The idea of treating strategic investments as options was popularized by Timothy Luehrman [38] in two HBR articles: [12] "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. [39] Reflecting the "mainstreaming" of ROV, Professor Robert C. Merton discussed the essential points of Arundel in his Nobel Prize Lecture in 1997. [40] 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

Related Research Articles

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Valuation (finance) process of estimating what something is worth, used in the finance industry

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Lattice model (finance) method for evaluating stock options that divides time into discrete intervals

In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise., though methods now exist for solving this problem.

Intellectual property assets such as patents are the core of many organizations and transactions related to technology. Licenses and assignments of intellectual property rights are common operations in the technology markets, as well as the use of these types of assets as loan security. These uses give rise to the growing importance of financial valuation of intellectual property, since knowing the economic value of patents is a critical factor in order to define their trading conditions.

The following outline is provided as an overview of and topical guide to finance:

The fuzzy pay-off method for real option valuation is a new method for valuing real options, created in 2008. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project. The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem.

The Datar–Mathews method is a method for real options valuation. The method provides an easy way to determine the real option value of a project simply by using the average of positive outcomes for the project. The method can be understood as an extension of the net present value (NPV) multi-scenario Monte Carlo model with an adjustment for risk aversion and economic decision-making. The method uses information that arises naturally in a standard discounted cash flow (DCF), or NPV, project financial valuation. It was created in 2000 by Professor Vinay Datar, Seattle University, and Scott H. Mathews, Technical Fellow, The Boeing Company.

In finance, a contingent claim is a derivative whose future payoff depends on the value of another “underlying” asset, or more generally, that is dependent on the realization of some uncertain future event. These are so named, since there is only a payoff under certain contingencies. Any derivative instrument that is not a contingent claim is called a forward commitment. The prototypical contingent claim is an option, the right to buy or sell the underlying asset at a specified exercise price by a certain expiration date; whereas (vanilla) swaps, forwards, and futures are forward commitments, since these grant no such optionality. Contingent claims are applied under financial economics in developing models and theory, and in corporate finance as a valuation framework.

References

  1. 1 2 3 Adam Borison (Stanford University). Real Options Analysis: Where are the Emperor's Clothes?.
  2. 1 2 3 Campbell, R. Harvey. Identifying real options, Duke University, 2002.
  3. Nijssen, E. (2014)Entrepreneurial Marketing; an effectual approach. Chapter 2, Routelegde, 2014.
  4. Amram, M., and K. N. Howe (2003), Real Options Valuations: Taking Out the Rocket Science, Strategic Finance, Feb. 2003, 10-13.
  5. Locatelli, Giorgio; Boarin, Sara; Pellegrino, Francesco; Ricotti, Marco E. (2015-02-01). "Load following with Small Modular Reactors (SMR): A real options analysis" (PDF). Energy. 80: 41–54. doi:10.1016/j.energy.2014.11.040. hdl:11311/881391.
  6. See Bilkic et. al. under #Applications.
  7. 1 2 Justin Pettit: Applications in Real Options and Value-based Strategy; Ch.4. in Trigeorgis (1996)
  8. 1 2 Joanne Sammer: Thinking in Real (Options) Time, businessfinancemag.com
  9. 1 2 3 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.
  10. This section draws primarily on Campbell R. Harvey: Identifying Real Options.
  11. This sub-section is additionally based on Aswath Damodaran: The Option to Expand and Abandon.
  12. 1 2 3 4 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.
  13. Aswath Damodaran: Risk Adjusted Value; Ch 5 in Strategic Risk Taking: A Framework for Risk Management. Wharton School Publishing, 2007. ISBN   0-13-199048-9
  14. See: §32 "Certainty Equivalent Approach" & §165 "Risk Adjusted Discount Rate" in: Joel G. Siegel; Jae K. Shim; Stephen Hartman (1 November 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 . Retrieved 12 November 2011.
  15. Aswath Damodaran: Valuing Firms in Distress.
  16. Dan Latimore: Calculating value during uncertainty. IBM Institute for Business Value
  17. 1 2 Lenos Trigeorgis, Rainer Brosch and Han Smit. Stay Loose, copyright 2010 Dow Jones & Company.
  18. 1 2 3 4 5 Michael J. Mauboussin, Credit Suisse First Boston, 1999. Get Real: Using Real Options in Security Analysis
  19. Tan, Jackson J.; Trinidad, Fernando L. (2018-02-15). "A real options model for loan portfolios of actively traded Philippine universal banks". Journal of Global Entrepreneurship Research . 8: 4. doi:10.1186/s40497-018-0091-9. ISSN   2251-7316.
  20. Tan, Jackson J.; Trinidad, Fernando L. (January 3, 2019). "Comparing Theory With Reported Data for Reliability: Real Options Modeling of Actively Traded Philippine Universal Banks - SAGE Research Methods". methods.sagepub.com. SAGE. Retrieved 2019-01-05.
  21. 1 2 3 4 5 6 7 Copeland, T.; Tufano, P. (2004). "A Real-World Way to Manage Real Options". Harvard Business Review . 82: 3.
  22. 1 2 3 Jenifer Piesse and Alexander Van de Putte. (2004). "Volatility estimation in Real Options". 8th Annual International Conference on Real Options
  23. 1 2 3 4 5 Damodaran, Aswath (2005). "The Promise and Peril of Real Options" (PDF). NYU Working Paper (S-DRP–05-02).
  24. Tan, Jackson J. (2018-01-01). "Interfaces for enterprise valuation from a real options lens". Strategic Change. 27 (1): 69–80. doi:10.1002/jsc.2181. ISSN   1099-1697.
  25. Cobb, Barry; Charnes, John (2004). "Real Options Volatility Estimation with Correlated Inputs". The Engineering Economist. 49 (2). Retrieved 30 January 2014.
  26. Cortazar, Gonzalo (2000). "Simulation and Numerical Methods in Real Options Valuation". EFMA 2000 Athens. SSRN   251653 .
  27. 1 2 Gilbert, E (2004). "An Introduction to Real Options" (PDF). Investment Analysts Journal . 33 (60): 49–52. doi:10.1080/10293523.2004.11082463.
  28. See pg 26 in Marion A. Brach (2003). Real Options in Practice. Wiley. ISBN   0471445568.
  29. 1 2 See Ch. 23, Sec. 5, in: Frank Reilly, Keith Brown (2011). "Investment Analysis and Portfolio Management." (10th Edition). South-Western College Pub. ISBN   0538482389
  30. Marco Dias. Real Options with Monte Carlo Simulation Archived 2010-03-18 at the Wayback Machine
  31. Cortazar, Gonzalo; Gravet, Miguel; Urzua, Jorge (2008). "The valuation of multidimensional American real options using the LSM simulation method" (PDF). Computers & Operations Research. 35: 113–129. doi:10.1016/j.cor.2006.02.016.
  32. Brennan, J.; Schwartz, E. (1985). "Evaluating Natural Resource Investments". The Journal of Business . 58 (2): 135–157. doi:10.1086/296288. JSTOR   2352967.
  33. Datar, V.; Mathews, S. (2004). "European Real Options: An Intuitive Algorithm for the Black Scholes Formula". Journal of Applied Finance. 14 (1). SSRN   560982 .
  34. Mathews, S.; Datar, V. (2007). "A Practical Method for Valuing Real Options: The Boeing Approach". Journal of Applied Corporate Finance . 19 (2): 95–104. doi:10.1111/j.1745-6622.2007.00140.x.
  35. 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. CiteSeerX   10.1.1.534.2962 . doi:10.1155/2009/238196.
  36. Ronald Fink: Reality Check for Real Options, CFO Magazine, September, 2001
  37. See Marco Dias: Does Risk-Neutral Valuation Mean that Investors Are Risk-Neutral? Archived 2010-07-16 at the Wayback Machine , Is It Possible to Use Real Options for Incomplete Markets?
  38. valuebasedmanagement.net
  39. Timothy A. Luehrman and William A. Teichner: "Arundel Partners: The Sequel Project." Harvard Business School Publishing case no. 9-292-140 (1992)
  40. Robert Merton, Nobel Lecture: Applications of Option-Pricing Theory: Twenty-Five Years Later, Pages 107, 115; reprinted: American Economic Review , American Economic Association, vol. 88(3), pages 323–49, June.

Further reading

Applications:

Theory

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