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.[3] For example, real options valuation could examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory.[4]

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.[5] 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.[6]

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 deal with various uncertainties in making decisions about the allocation of resources among R&D projects.[7][8][9][10] Non business examples might be evaluating the cost of cryptocurrency mining machines,[11] or the decision to join the work force, or rather, to forgo several years of income to attend graduate school.[12] 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.[13][14][15] 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.[16]

Types of real options

Simple Examples

This simple example shows the relevance of the real option to delay investment and wait for further information, and is adapted from "Investment Example"..

Consider a firm that has the option to invest in a new factory. 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"..

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.[17] 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.[18]

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. As in the preceding cases, this flexibility increases the value of the project, corresponding in turn, to the "premium" paid for the real option.


Given the above, it is clear that there is an analogy between real options and financial options,[20] 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 (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. [21] [22] [23] 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. [24] [25]

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.[26] 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.[27] 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.[28]) 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.[29]

Options based valuation

Although there is much similarity between the modelling of real options and financial options,[20][30] 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.[31][32] 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...[30]

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.[33]

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.[20][30][31][34] The specific application, though, is as follows:

Valuation methods

The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options.[36][37] 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.

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,[43][44] fuzzy pay-off method,[45] the simulation with optimised exercise thresholds method.[3]


The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations.[46] 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

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" [27] 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",[27] and may be less relevant otherwise.[32] 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.[16] 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. [47] 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.[16]
  3. Theoretical difficulties, which are more serious, may also arise.[48]
  • 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,[34] 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:.[30]
  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.[30]
  • 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.[30][39] 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. (For an alternative, modifying Black-Scholes, see: [34].)


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.[27] 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.[26] 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.[13][14] The idea of treating strategic investments as options was popularized by Timothy Luehrman[49] in two HBR articles:[20] "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.[50] Reflecting the "mainstreaming" of ROV, Professor Robert C. Merton discussed the essential points of Arundel in his Nobel Prize Lecture in 1997.[51] 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


  1. ^ a b c Adam Borison (Stanford University). Real Options Analysis: Where are the Emperor's Clothes?.
  2. ^ a b c Campbell, R. Harvey. Identifying real options, Duke University, 2002.
  3. ^ a b c Locatelli, Giorgio; Mancini, Mauro; Lotti, Giovanni (2020-04-15). "A simple-to-implement real options method for the energy sector". Energy. 197: 117226. doi:10.1016/ ISSN 0360-5442. S2CID 213872142. Archived from the original on 4 May 2020.
  4. ^ Nijssen, E. (2014). Entrepreneurial Marketing; an effectual approach. Chapter 2, Routelegde, 2014.
  5. ^ Amram, M., and K. N. Howe (2003), Real Options Valuations: Taking Out the Rocket Science, Strategic Finance, Feb. 2003, 10-13.
  6. ^ 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/ hdl:11311/881391.
  7. ^ Trigeorgis, Lenos; Reuer, Jeffrey J. (2017). "Real options theory in strategic management". Strategic Management Journal. 38 (1): 42–63. doi:10.1002/smj.2593. ISSN 1097-0266.
  8. ^ Oriani, Raffaele; Sobrero, Maurizio (2008). "Uncertainty and the market valuation of R&D within a real options logic". Strategic Management Journal. 29 (4): 343–361. doi:10.1002/smj.664. ISSN 1097-0266.
  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. 56 (5): 1000–1039. doi:10.1111/joms.12423. 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. 25 (1): 1–21. doi:10.1002/smj.358. ISSN 0143-2095.
  11. ^ Yaish, Aviv; Zohar, Aviv (2020-06-18). "Pricing ASICs for Cryptocurrency Mining". arXiv:2002.11064. ((cite journal)): Cite journal requires |journal= (help)
  12. ^ See Bilkic et al. under #Applications.
  13. ^ a b Justin Pettit: Applications in Real Options and Value-based Strategy; Ch.4. in Trigeorgis (1996)
  14. ^ a b Joanne Sammer: Thinking in Real (Options) Time,
  15. ^ David Shimko (2009). Real Options: Opportunity from Risk. archived 2010-04-05.
  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. S2CID 15362734.
  17. ^ This section draws primarily on Campbell R. Harvey: Identifying Real Options.
  18. ^ This sub-section is additionally based on Aswath Damodaran: The Option to Expand and Abandon.
  19. ^ 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/
  20. ^ 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.
  21. ^ 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
  22. ^ 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.
  23. ^ Aswath Damodaran: Valuing Firms in Distress.
  24. ^ Michael C. Ehrhardt and John M. Wachowicz, Jr (2006). Capital Budgeting and Initial Cash Outlay (ICO) Uncertainty. Financial Decisions, Summer 2006.
  25. ^ Dan Latimore: Calculating value during uncertainty. IBM Institute for Business Value
  26. ^ a b Lenos Trigeorgis, Rainer Brosch and Han Smit. Stay Loose, copyright 2010 Dow Jones & Company.
  27. ^ a b c d e Michael J. Mauboussin, Credit Suisse First Boston, 1999. Get Real: Using Real Options in Security Analysis
  28. ^ 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.
  29. ^ 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". SAGE. Retrieved 2019-01-05.
  30. ^ a b c d e f g Copeland, T.; Tufano, P. (2004). "A Real-World Way to Manage Real Options". Harvard Business Review. 82 (3): 90–9, 128. PMID 15029793.
  31. ^ a b c Jenifer Piesse and Alexander Van de Putte. (2004). "Volatility estimation in Real Options". 8th Annual International Conference on Real Options
  32. ^ a b c d e Damodaran, Aswath (2005). "The Promise and Peril of Real Options" (PDF). NYU Working Paper (S-DRP-05-02).
  33. ^ 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.
  34. ^ a b c Pablo Fernandez (2019). "Valuing Real Options: Frequently Made Errors". SSRN 274855.
  35. ^ Cobb, Barry; Charnes, John (2004). "Real Options Volatility Estimation with Correlated Inputs". The Engineering Economist. 49 (2): 119–137. doi:10.1080/00137910490453392. S2CID 154342832. Retrieved 30 January 2014.
  36. ^ Cortazar, Gonzalo (2000). "Simulation and Numerical Methods in Real Options Valuation". EFMA 2000 Athens. SSRN 251653.
  37. ^ a b Gilbert, E (2004). "An Introduction to Real Options" (PDF). Investment Analysts Journal. 33 (60): 49–52. doi:10.1080/10293523.2004.11082463. S2CID 166808417.
  38. ^ See pg 26 in Marion A. Brach (2003). Real Options in Practice. Wiley. ISBN 0471445568.
  39. ^ 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
  40. ^ Marco Dias. Real Options with Monte Carlo Simulation Archived 2010-03-18 at the Wayback Machine
  41. ^ 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. hdl:10533/139003.
  42. ^ Brennan, J.; Schwartz, E. (1985). "Evaluating Natural Resource Investments". The Journal of Business. 58 (2): 135–157. doi:10.1086/296288. JSTOR 2352967.
  43. ^ Datar, V.; Mathews, S. (2004). "European Real Options: An Intuitive Algorithm for the Black Scholes Formula". Journal of Applied Finance. 14 (1). SSRN 560982.
  44. ^ 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.
  45. ^ 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 doi:10.1155/2009/238196.
  46. ^ Ronald Fink: Reality Check for Real Options, CFO Magazine, September, 2001
  47. ^ Don M. Chance and Pamela P. Peterson (2002). Real Options and Investment Valuation. The Research Foundation of AIMR
  48. ^ 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?
  49. ^
  50. ^ Timothy A. Luehrman and William A. Teichner: "Arundel Partners: The Sequel Project." Harvard Business School Publishing case no. 9-292-140 (1992)
  51. ^ 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

Standard texts:




Calculation resources