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In corporate finance, real options analysis or ROA (not to be confused with return on assets) applies put option and call option valuation techniques to capital budgeting decisions.[1] A real option itself, is the right — but not the obligation — to undertake some business decision; typically the option to make, abandon, expand, or shrink a capital investment. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real option.

ROA, as a discipline, extends from its application in Corporate Finance, to decision making under uncertainty in general, adapting the mathematical techniques developed for financial options to "real-life" decisions. For example, R&D managers can use Real Options Analysis to help them determine where to best invest their money in research; a non business example might be the decision to join the work force, or rather, to forgo several years of income and to attend graduate school. Thus, in that it forces decision makers to be explicit about the assumptions underlying their projections, ROA is increasingly employed as a tool in business strategy formulation.[2]


Comparison with standard techniques

ROA is often contrasted with more standard techniques of capital budgeting, such as net present value (NPV), where only the most likely or representative outcomes are modelled, and the "flexibility" available to management is thus "ignored"; see Valuing flexibility under Corporate finance. The NPV framework therefore (implicitly) assumes that management will be "passive" as regards their Capital Investment once committed, whereas ROA assumes that they will be "active" and may / can modify the project as necessary. The real options value of a project is thus always higher than the NPV - the difference is most marked in projects with major uncertainty (as for financial options higher volatility of the underlying leads to higher value).

More formally, the treatment of uncertainty inherent in investment projects differs as follows. Under ROA, uncertainty inherent is usually accounted for by risk-adjusting probabilities (a technique known as the equivalent martingale approach). Cash flows can then be discounted at the risk-free rate. Under DCF analysis, on the other hand, this uncertainty is accounted for by adjusting the discount rate, (using e.g. the cost of capital) or the cash flows (using certainty equivalents, or applying "haircuts" to the forecast numbers). These methods normally do not properly account for changes in risk over a project's lifecycle and fail to appropriately adapt the risk adjustment.


As above, ROA is distinguished from other approaches in that it takes into account uncertainty about the future evolution of the parameters that determine the value of the project, and management's ability to respond to the evolution of these parameters. It is the combined effect of these, that makes ROA technically more difficult than its alternatives. Essentially:

  • The project is modelled in terms of:
    • uncertainty: the volatility in the change in value over time is usually proxied as the volatility of project NPV;
    • value: the starting value (spot price) is usually proxied via management's best guess as to NPV.
  • Management's ability to respond to changes in value is modeled at each decision point as a series of:

Valuation methods

The valuation methods employed are generally adapted from techniques developed for valuing financial options. The most commonly employed are Closed form solutions - often modifications to Black Scholes - and binomial lattices; the latter are probably more widely used due to their flexibility. Specialised Monte Carlo Methods have also been developed and are increasingly applied particularly to high dimensional problems. 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 ROA articles discussed this method, its use is relatively uncommon today - particularly amongst practitioners - due to the required mathematical sophistication. For a general discussion, see Option (finance): Model implementation.

In general, these methods are limited either as regards dimensionality, or as regards early exercise, or both; in selecting a model, analysts must usually trade off between these considerations. Additionally, sometimes, the stochastic nature of such projections can make analysis using the Monte Carlo method infeasible, necessitating other investigatory methods, such as Robinson differentials. Other new methods have recently been introduced to simplify the calculation of the real option value and thus make the numerical use of the methods easier for practitioners; these include the Datar-Mathews method (2004,2007) and the Fuzzy Pay-Off Method for Real Option Valuation (2008).


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 tradeable - e.g. the factory owner cannot easily sell the factory upon which he has the option. This results in difficulties as to estimating the value (i.e. spot price) and volatility of the underlying which are key valuation inputs - this is further complicated by uncertainty as to management's actions in the future. Further, difficulties arise in applying the rational pricing assumptions which underpin these option models: often the "replicating portfolio approach", as opposed to Risk neutral valuation, must be applied.

Additional difficulties include the fact that the real option itself is also not tradeable — e.g. the factory owner cannot sell the right to extend his factory to another party, only he can make this decision; however, some real options can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the future. Some real options are proprietary (owned or exercisable by a single individual or a company); others are shared (can be exercised by many parties). Therefore, a project may have a portfolio of embedded real options; some of them can be mutually exclusive.

In general, since ROA attempts to predict the future, the quality of the output will only ever be as good as the quality of the inputs, which by their nature are sketchy. This is also valid for net present value analysis, but this technique does not require volatility information. Opinion is therefore divided as to whether Real Options Analysis provides genuinely useful information to real-world practitioners.


Whereas business operators have been making capital investment decisions for centuries, the term "real option" is relatively new, and was coined by Professor Stewart Myers at the MIT Sloan School of Management in 1977. It is interesting to note though, that 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" itself is closely tied to these new methods.

Real options are today an active field of academic research. Professor Eduardo Schwartz (UCLA) was a pioneering academic in the field. Professor Lenos Trigeorgis (University of Cyprus) has been a leading name for many years, publishing several influential books and academic articles. 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, the chief U.S. investment strategist for Credit Suisse First Boston and an adjunct professor of finance at the Columbia Business School. Mauboussin uses real options in part to explain the gap between how the stock market prices some businesses and the "intrinsic value" for those businesses as calculated by traditional financial analysis, specifically using discounted cash flows. Trigeorgis also has broadened exposure to real options through layman articles in publications such as The Wall Street Journal[3]. This popularization is such that ROA is now a standard offering in postgraduate finance degrees, and often, even in MBA curricula at many Business Schools.

Recently, in business strategy, real options have been deployed in the construction of an "option space", where volatility is compared with value-to-cost.

See also



  1. ^ Campbell, R. Harvey. "Identifying real options" , Duke University, 2002.
  2. ^ See, for example, Applications in Real Options and Value-based Strategy, Justin Pettit; Ch.4. in Trigeorgis (1996)
  3. ^


  • Amram, Martha; Kulatilaka,Nalin (1999). Real Options: Managing Strategic Investment in an Uncertain World. Boston: Harvard Business School Press. ISBN 0-87584-845-1. 
  • Copeland, Thomas E.; Vladimir Antikarov (2001). Real Options: A Practitioner's Guide. New York: Texere. ISBN 1-587-99028-8. 
  • Dixit, A.; R. Pindyck (1994). Investment Under Uncertainty. Princeton: Princeton University Press. ISBN 0-691-03410-9. 
  • Moore, William T. (2001). Real Options and Option-embedded Securities. New York: John Wiley & Sons. ISBN 0-471-21659-3. 
  • Müller, Jürgen (2000). Real Option Valuation in Service Industries. Wiesbaden: Deutscher Universitäts-Verlag. ISBN 3-824-47138-8. 
  • Smit, T.J.; Trigeorgis, Lenos (2004). Strategic Investment: Real Options and Games. Princeton: Princeton University Press. ISBN 0-691-01039-0. 
  • Trigeorgis, Lenos (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge: The MIT Press. ISBN 0-262-20102-X. 

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