Bob Jensen's Threads on Real Options, Option Pricing Theory, and Arbitrage Pricing Theory 

Bob Jensen at Trinity University

Bob Jensen's threads on accounting for stock options ---

Real Options Valuation ---

Real Options
by Vladimir Antikarov and Thomas E. Copeland
ISBN: 1587991861 Hard Cover 9/1/2003

This revised edition of the highly successful book, Real Options, offers corporate decision-makers the ability to assess the profitability of their ventures and decide which avenue of expansion or investment to go down and, crucially, when to take that leap. The reader goes on a journey through real options, from the basics to more advanced topics such as options and game theory. It provides expert guidance on how to implement the theory to maximize investment opportunities by utilizing uncertainty as an asset and reducing downside risk.

Jacket Description:
Determining the feasibility and the priority of potential investments is critical in business decision making. A new method for estimating the value of investments -- real options -- is gaining ground over the traditional approach of calculating net present value (NPV). Tom Copeland and Vladimir Antikarov argue that in ten years real options will replace NPV as the central paradigm for investment decisions. This book offers the first practitioner's guide for understanding and implementing real options in everyday decision making. The authors bring years of experience with dozens of corporations in implementing real options. Copeland and Antikarov show how NPV is flawed and tends to undervalue investment opportunities. NPV is a static calculation that fails to consider the many options that management has over the lifetime of an investment project. Such options include expanding or extending the project if results are better than expected or scaling down or abandoning the project if it turns out to be worse than expected. There are chapters that deal with valuing various types of simple options, such as deferral, abandonment, expansion, and contraction of projects, and more advanced options such as compound and switching options. Chapter 2 shows how Airbus Industrie uses real options in its marketing efforts and discusses the difficulties encountered in implementing real options. Chapter 7 shows how to write an Excel spreadsheet to value simple options, combinations of them, and compound options. Chapters 9 and 10 discuss ways of modeling uncertainties. The analysis is enriched with case histories and case solutions. The end-of-chapter questions and problems provide both experience and additional insights into the application of real options. The authors also offer solutions to the questions posed in the book, as well as real option models useful to the would-be practitioner on their Web site, .


"Real option analysis of aircraft acquisition: A case study," by Qiwei Hu and Anming Zhang, Journal of Air Transport Management, Volume 46, July 2015, Pages 19–29 ---

This paper demonstrates that aircraft acquisition by airlines may contain a portfolio of real options (flexible strategies) embedded in the investment's life cycle, and that if airlines rely solely on the static NPV method, they are likely to underestimate the true investment value. Two real options are investigated: i) the “shutdown-restart” option (a carrier may shutdown a plane if revenues are less than costs, but restarts it if revenues are more than costs), and ii) the option to defer aircraft delivery. We quantify the values of these options in a case study of a major U.S. airline. The economic insight could help explain observed capital expenditures of airlines, and serve as a rule of thumb in evaluating capital budgeting decisions. A compound option (consisting of both the shutdown-restart and defer options) is also analyzed.

Airbus and Boeing: Superjumbo Decisions
by Samuel E BodilyKenneth C. Lichtendahl
Harvard Case

Real Options Valuation Limitations ---

Jensen Comment
Many moons ago, Stewart Myers and I were in a doctoral program together at Stanford University. After graduation, Stewart became one of the most outstanding economics and financial researchers of the world --- 

The term "real options" can be attributed to the Stewart Myers ("Determinants of Capital Borrowing", Journal of Financial Economics, Vol..5, 1977). The theory of real options extends the concept of financial options (in particular call options) into the realm of capital budgeting under uncertainty and valuation of corporate assets or entire corporations.

The real options approach is dynamic in the sense that includes the effect of uncertainty along the time, and what/how/when the relevant real options shall be exercised. Some argue that real options do little more than can be done with dynamic programming of investment states under uncertainty, real options add a rich economic theory to capital investing under uncertainty.

The real options problem can be viewed as a problem of optimization under uncertainty of a real asset (project, firm, land, etc.) given the available options. Since I have been asked to teach a bit about real options theory while I am lecturing at Monterrey Tech I thought I might share a bit of my source material that I discovered on the Web.

Competitive Strategies: Options and Games by Benoit Chevalier-Roignant and Lenos Trigeorgis (MIT Press; 488 pages; $55). Combines the decision-making approaches of real options and game theory.

Amazon's reviews are strong but possibly biased

Competitive Strategies: Options and Games by Benoit Chevalier-Roignant and Lenos Trigeorgis (MIT Press; 488 pages; $55). Combines the decision-making approaches of real options and game theory.

Amazon's reviews are strong but possibly biased

Accounting for Fixed Assets and Investment Efficiency: A Real Options Framework

Accounting and Business Research, Forthcoming

56 Pages
Posted: 9 Oct 2019

Lufei Ruan

San Francisco State University

Date Written: September 27, 2019


In a perfect world, a manager's investment in fixed assets would increase with the assets' profitability. However, when managers privately know their project profitability and care about their company’s short-term share price, managers of less profitable firms face the temptation to overinvest in order to pool with strong firms. This creates pressure on strong firms to overinvest to the point where weak firms cease to find it worthwhile to mimic strong firms. I show that, when firms have abandonment options, the willingness of a weak firm's manager to mimic depends on the expected future resale value of the fixed assets. An impairment policy (prohibiting write-ups) reduces the value of abandonment options, which are particularly important for weak firms. The reduced value of the abandonment options decreases the amount of overinvestment required by strong firms to separate themselves from weak firms. I also show that allowing firms to choose depreciation schedules improves investment efficiency: in equilibrium, strong firms choose faster depreciation. Last, in the staged-investments setting, I show that an impairment policy also mitigates underinvestment at an initial stage. These findings rationalize the current accounting standards for fixed assets and contribute to related policy debates on accounting measurement.

Keywords: accounting for fixed assets, conservatism, investment efficiency, abandonment options, staged investments, real options

JEL Classification: G31, M41, M48

Real Options are mentioned in the FASB's "Special Report: Business and Financial Reporting, Challenges from the New Economy," by Wayne Upton, Financial Accounting Standards Board, Document 219-A, April 2000 ---  (Like so many older Rutgers FASB links the link is broken and lost forever)

Wayne Upton wrote as follows on pp. 91-93:

Measurement and Real Options

Perhaps the most promising area for valuation of intangible assets is the developing literature in valuation techniques based on the concept of real options. Techniques using real options analysis are especially useful in estimating the value of intangible assets that are under development and may not prove to be commercially viable.

A real option is easier to describe than to define. A financial option is a contract that grants to the holder the right but not the obligation to buy or sell an asset at a fixed price within a fixed period (or on a fixed date). The word option in this context is consistent with its ordinary definition as “the power, right or liberty of choosing.” Real option approaches attempt to extend the intellectual rigor of option-pricing models to valuation of nonfinancial assets and liabilities. Instead of viewing an asset or project as a single set of expected cash flows, the asset is viewed as a series of compound options that, if exercised, generate another option and a cash flow. That’s a lot to pack into one sentence. In the opening pages of their recent book, consultant Martha Amram and Boston University professor Nalin Kulatilaka offer five examples of business situations that can be modeled as real options: 56

• Waiting to invest options, as in the case of a tradeoff between immediate plant expansion (and possible losses from decreased demand) and delayed expansion (and possible lost revenues)

• Growth options, as in the decision to invest in entry into a new market

• Flexibility options, as in the choice between building a single centrally located facility or building two facilities in different locations

• Exit options, as in the decision to develop a new product in an uncertain market

• Learning options, as in a staged investment in advertising.

Real-options approaches have captured the attention of both managers and consultants, but they remain unfamiliar to many.

Proponents argue that the application of option pricing to nonfinancial assets overcomes the shortfalls of traditional present value analysis, especially the subjectivity in developing risk-adjusted discount rates. They contend that a focus on the value of flexibility provides a better measure of projects in process that would otherwise appear uneconomical. A real-options approach is consistent with either fair value (as described in Concepts Statement 7) or an entity-specific value. The difference, as with more conventional present value, rests with the selection of assumptions. If a real option is available to any marketplace participant, then including it in the computation is consistent with fair value. If a real option is entity-specific, then a measurement that includes that option is not fair value, but may be a good estimate of entity-specific value.

Thank you for sharing Ulrich Hommel --- 

Real options capture the value of managerial flexibility to adapt decisions in response to unexpected market developments.

Companies create shareholder value by identifying, managing and exercising real options associated with their investment portfolio.

The real options method applies financial options theory to quantify the value of management flexibility in a world of uncertainty. If used as a conceptual tool, it allows management to characterize and communicate the strategic value of an investment project.

Traditional methods (e.g. net present value) fail to accurately capture the economic value of investments in an environment of widespread uncertainty and rapid change.

The real options method represents the new state-of-the-art technique for the valuation and management of strategic investments.

The real option method enables corporate decision-makers to leverage uncertainty and limit downside risk.

This site is maintained by Ulrich Hommel and the Chair of Investment and Risk Management of the European Business School (Oestrich- Winkel) as a free service to the scientific and management community. If you have any information on the real options method that you wish to make available to the public via this web site, please contact

M.Sc. Dissertation Abstract: Real Options in R&D Capital Budgeting - A Case Study at Pharmacy & Upjohn. By M.Sc. Gunnar Kallberg and M.Sc. Peter Laurin, from Gothenburg School of Economics and Commercial Law, Department of Economics, Sweden. The abstract can be found under Item 5 at 

Despite the wide use of the traditional capital budgeting techniques NPV, IRR, and Payback time among organizations, criticism have been raised against the static use of them. The techniques only use tangible factors and do not take into account intangible factors such as future competitive advantage, future opportunities, and managerial flexibility. A relatively new technique to capital budgeting is the real option approach. This approach has the potential to include the value of the project from active management and strategic interactions using the valuation technique for financial options.

The main objective of this thesis is to numerically analyze the value of an option approach in the capital budgeting of R&D investments. The results of the option approach will be compared with the results from traditional NPV approach. This will be done by constructing a valuation model and this model will then be numerically applied to a pharmaceutical R&D project at Pharmacia & Upjohn.

The model that we have constructed includes both the binomial and the Black & Scholes formula for the valuation of options. The binomial method is used in valuing the development phase of the R&D project and the Black & Scholes formula is used when valuing a follow-on project. A common spreadsheet program has been used to construct the model.

If you can overlook some of the English grammar mistakes (mainly when the authors' native language is something other than English), take a look at the following helpful free documents on the use of real options in capital budgeting.  

Real Options --- 

A great Website on real options --- 

Note especially the Visual FAQ's on Real Options --- 

Underlying all of this is Options Pricing Models and Arbitrage Pricing Theory.  In that realm, I have an aged (yellowed?) 1984 working paper that journal editors claimed they could just not understand and would not touch with a ten foot pole.  Am I the only one who finds my stuff to be crystal clear?

Working Paper 149
Does a Ross Economy Lunch Really Cost as Much as Hirshleifer Cuisine Complete With Sigma Squared for Dessert?

You can find more about such things in papers and books that really did get published in such journals as those listed below:  

Accounting Theory

"CPAs Find 'Real Options' for Business Valuation," Journal of Accountancy, February 2002, Page 22 --- 

CPA valuators are increasingly finding that clients are asking for more than just a final number in their estimates. Instead, the market is pushing CPAs for a more holistic approach. And CPAs are responding with a new school of practice called real options theory.

“Real options theory is connected more to operational or corporate theories, as opposed to the financial aspects of the investing arena,” explains Steven E. Sacks, a CPA and the CPA2Biz senior product manager in charge of BV issues. “Heretofore, the recognized valuation methods have been inadequate for forecasting revenue streams and have completely ignored the opportunities management can avail themselves of through different courses of action.”

These different courses of action can result in a difference between the price of a business as measured by the stock market value and the intrinsic value, a concept typically used by financial analysts, explains Sacks, who was an advocate of the BV mission at the AICPA long before joining CPA2Biz.

Take some real world examples: Time Warner’s merger with AOL to expand its distribution network via an online environment. Yahoo!’s decision to extend its portal services into the Internet auction business. Or, eBay’s purchase of and Butterfield & Butterfield.

"The Lease Accounting Proposal: What Investors Say," by Tom Selling, The Accounting Onion, September 18, 2009 --- Click Here

In this post, I'll be reviewing two comment letters submitted to the FASB in response to its Discussion Paper (DP) on lease accounting* by the Investors Technical Advisory Committee (ITAC) of the FASB, and the CFA Institute Centre for Financial Market Integrity (CFA).   My original comments are here

The lease accounting project is a strong test of the proposition that accounting standards are capable of cutting through the camouflage of legal form to get at the underlying economics of an arrangement. In that respect, FAS 13 has been a dismal failure, with untold amounts of shareholder value being destroyed by management machinations aiming to exploit complex accounting loopholes and bright line rules lacking no conceptual basis.

Almost any new standard will be a significant improvement over FAS 13, so one of the dangers we face is setting the bar too low. For example, since FAS 13 was promulgated over 30 years ago, the field of financial management has progressed well beyond the point where precise measurement of lease value drivers is on the frontier of our knowledge. I'm not just talking about academic theorizing, either. According to the book, Real Options: A Practitioner's Guide, economic valuation of complex lease terms was first undertaken by executives at Airbus, who needed to know the true cost of the flexibility they were writing into their leases to accommodate their customers' risk preferences. That was over twenty years ago! I'm certainly don't consider myself to be at the cutting edge of financial modeling, but give me about a week, and I should be able to write a spreadsheet to value leased assets and lease obligations that can capture 100% of a lease's complexity for more than 90% of the leases out there.

So, given the state of the art of leasing and finance, we should be expecting a lot more from the FASB than the usual medley of incremental piecemeal improvements they are proposing. We should not just expect that: (1) the assets and liabilities arising from leasing arrangements are appropriately measured on the balance sheet; but (2) that they should also be appropriately measured. As I will be describing, below, ITAC and CFA are pressing for (1), but are aiming far too low on (2). Ironically, given the prominence and reputation for integrity of ITAC and CFA groups, one thing that you can take to the bank is that their positions will be regarded as the upper bound on the concessions to investors that will come out of the final standard. Thus, the most to be had is recognition of leases on the balance sheet; but they will be reported as arbitrary numbers based on calculations that hearken back to the relative stone ages of financial management.

I'll now discuss some of the specific issues starting with the ones I have the least qualms about, and ending with the stuff that gets my goat.

Overall Approach to Lease Accounting

The DP proposes to eliminate operating lease accounting, with the exception of "non-core" and short-term leases. While both ITAC and CFA strongly support the elimination of operating lease accounting, they are both against the notion of a "non-core leases" category. Nobody would ever expect that lease capitalization would have to be applied to immaterial items; but whatever "non-core" is supposed to mean, it doesn't always correspond to "immaterial." It's a ridiculously silly notion, but I'll nonetheless award points to both groups for pointing that out—much more tactfully than I would be capable of doing.

ITAC further adds that exempting short-term leases would be an open invitation to gaming, which surely must have been obvious to the FASB but somebody needed to mention it.

Scope of a Forthcoming Standard

Without calling out the FASB for the real reason that lessor accounting issues were deferred, CFA reluctantly accepts the FASB's decision to defer consideration of lessor accounting. The real reason for the limited scope goes something like this: 'We're already taking too much heat from financial institutions on loan accounting, so let's not mess with them any more than we have to.' ITAC, for my tastes, is being too conciliatory (perhaps trying to rebuild the bridges it has burned on IFRS and fair value?) when they state that they are content for now to focus on lessee accounting.

My own two cents — If there is any area in which balance sheet accounting standards can (and should be) symmetrical, leasing is it. If the FASB is serious about its commitment to an asset/liability view of recognition and measurement, then the only real revenue recognition issue in leasing is nothing more than how to present changes in lease-related assets and liabilities on the income statement. I would not object to deferral of income statement presentation issues from the scope of the next major accounting standard on leases, but I'm disappointed that ITAC and CFA are not exhorting the FASB to get everyone's balance sheet right. Let the big boy lessors present their income statement any old way they want; and let's require detailed roll-forward disclosures of the changes in the balance sheet amounts.



Everything I have written to this point has been little more than caviling, compared to my consternation on the groups' positions regarding measurement. CFA states that discounting at the incremental borrowing rate would yield a reasonable approximation of fair value, even when there is "significant uncertainty." That's the great unsupported statement of their comment letter—probably because no support is possible.

In the years since FAS 13, alternatives to discounted cash flow (DCF) analysis have been sought and developed because one eventually had to acknowledge a truth that is exactly the opposite of what CFA claims to believe: the truth is that picking the discount rate to value contingent cash flows, and coming up with a reliable measure of the fair value** of those cash flows, is nothing more than a guessing game. Ad hoc adaptations of discounted cash flow DCF modeling to option-ladened arrangements is so yesterday. That the FASB proposes to go back to the stone ages of financial theory is less surprising to me than learning that both CFA and ITAC are cool with their doing it.

Here's a much more robust way to think about lease valuation. There are three categories of cash flows in leasing arrangements: (1) the unconditional rental payments to be made, (2) required payments whose amount is determined by reference to uncertain future events, and (3) optional payments. We should require that a preparer document and disaggregate the fair value of their leases by each of these components. This can only mean that options must be valued using option pricing models—i.e., nails should be driven with a hammer. Yes, not all of the cash flow elements of a lease are mutually exclusive, but modern valuation models take care of that. Disaggregation in disclosure of interrelated items is challenging, but reasonable assumptions can be made and disclosed.

As to separate measurement of options, the FASB suggests, and both CFA and ITAC don't object to, a version of DCF that truncates the expected cash flows at the "most likely lease term." Given the financial technology nearly everyone has at their disposal, it's a ludicrous suggestion. Therefore, I expect it will be embraced universally by issuers. That alone should cause CFA and ITAC to question their judgment in this regard.

ITAC supports the most likely lease term rule of thumb (incredibly, they elevate it to "principle" status in their comments), because it seems that everybody should be able to do it. So, not only are they proposing to pound nails with rocks instead of hammers, they don't think it's worth the effort to drive the nail flush. Who are we writing standards for? FASB ought to be thinking first of the Fortune 500, because that's the bulk of the U.S. economy. Simplistic models to accommodate smaller companies no longer make sense from a cost-benefit perspective.

CFA states that one reason they support the expected lease term approach is out of expediency: "…an acceptable alternative in the interim until the use of fair value for non-financial assets is addressed by standard setters." And when will fair value for non-financial assets be addressed by standard setters? Given the glacial pace of standard setting, and the priorities that standard setters seem to have set for themselves, I'm giving even money that we won't have a general standard on that for at least another 20 years; and 2:1 odds that it won't happen before hell freezes over.  Is that really how long the CFA is willing to wait.

The bottom line on the measurement issue is that if the FASB requires some ad hoc discounted cash flow model for measuring leases on financial statements, then one of two things are going to happen: either companies will have to measure leases twice – the approach they use for internal decision-making, and again with the FASB's stone age approach – or companies will throw out the approach they use for internal decision making and base their decision entirely on how a lease will be portrayed in the financial statements. Neither alternative should be acceptable to CFA or ITAC.

And that brings me to my bottom line on the CFA and ITAC comment letters. Both groups are legitimately concerned about the quality of information that investors will get from a new lease accounting standard, and they evidently believe that getting leases on the balance sheet at any number is as much as they dare hope for without rocking the boat too much. However, both groups virtually ignore the potentially huge value that investors will realize if the new leasing standard leads to better decision making by managers. Assets that should be leased will be leased, and assets that should be bought will be bought. That can only be fully realized if lease accounting gets both recognition and measurement as right as it can be. CFA and ITAC need to hold the FASB's feet to the fire, because nobody will do it for them.

Finally, here's my message for the FASB. Elimination of operating lease accounting is a good thing; it will certainly cut into the book of business of financial engineers and lawyers who accomplish little else than meeting management's financial reporting objectives by skirting the edges of the bright lines. But, if you choose to catapult lease measurement back to the stone ages, all you will accomplish is inviting those same advisors to adapt to a new game at shareholders' expense. You will not be pleased to eventually discover that, once again and forevermore, you will find yourself chasing your own tail to issue fresh interpretations of unprincipled rules to stop some of more egregious ploys; and worse, you will be pressured to issue new interpretations to widen some of the inherent loopholes in stone age valuation. In the process, your policy choices will surely destroy value for shareholders (although you will strenuously deny it).

Alternatively, you can craft a principled and perforce simple standard requiring economic valuation of leases. There will be some work to do in specifying the objectives of the measurement process, but you will actually be able to afford flexibility in the choice of models and parameter selection. If you do that, some managers will pay consultants, but it will be for honest advice from valuation experts; they could also eschew professional advice and negotiate less complex lease terms that they can understand and value straightforwardly.  Honest advice is geared toward discovering the underlying economics of an arrangement, and it will cost a small fraction of the FAS 13-style advice. In the process of all this, your policy choices will create value for shareholders.  

But, don't just take my word for this. Credit Suisse analysts recently issued a report entitled, What if All Financial Instruments Were at Fair Value?" [I can't find it on the web, so I don't dare post a link to my own electronic copy] In it, I discovered a refreshing message that I hope ITAC, CFA and FASB will take to heart:

"With companies paying more attention to the fair values of their financial instruments, behavior could change. The controls that would need to be put in place and the due diligence involved could force companies to better understand their assets and liabilities. If that were to result in better management, companies could be rewarded with a lower cost of capital." [emphasis supplied]


Shalom, and L'shana Tovah (Happy New Year!)


*The IASB also has a DP out on the topic that is about 90% similar to the FASB's. So for simplicity, I just refer to the FASB's version from here on out.

**I am an ardent supporter of replacement cost measurements, especially for leases. For example, I haven't the slightest idea how the FASB is going to come up with an exit price concept for non-transferable leases. But, to avoid distractions from other points, I am going to presume solely for the sake of sidestepping this issue that all leases are transferable. It doesn't cause replacement cost and fair value to converge, but it gets us close enough for my purposes in this post.


September 18, 2009 reply from Bob Jensen

Hi Tom,

Readers that want to dig more into the history of Real Options, Option Pricing Theory, and Arbitrage Pricing Theory ---

I appreciate your heads up on the Copeland and Anticarov book. Tom Copeland is one of my favorite textbook writers.

Bob Jensen

Bob Jensen's threads on off-balance sheet financing are at


Books recommended by the Harvard University Project Finance Portal --- 

Real Option Analysis:

Amram, M., and N. Kulatilaka, 1999, Real Options: Managing Strategic Investment in an Uncertain World, (Harvard Business School Press, Boston, Mass.).

Brennan, M., and E. Schwartz, A New Way of Evaluating Natural Resource Investments, 1985, Midland Journal of Corporate Finance, 3, pp. 78-88.

Copeland, T., and P. Keenan, 1998, Making Real Options Real, The McKinsey Quarterly, No. 3, pp. 128-141.

Dixit, A. K., and R.S. Pindyk, 1994, Investment Under Uncertainty, (Princeton University Press, Princeton, New Jersey).

Dixit, A. K., and R.S. Pindyk, 1995, The Options Approach To Capital Investment, Harvard Business Review, May/June, pp. 105-115.

Kemna, A.G.Z., 1993, Case Studies On Real Options, Financial Management, Autumn, pp. 259-270

Kulatilaka, N., and A. Marcus, 1992, Project Valuation Under Uncertainty, Journal of Applied Corporate Finance, Fall, pp. 92-100.

Leslie, K., and M. Michaels, 1997, The Real Power of Real Options, The McKinsey Quarterly, No. 3.

Leslie, K., and M. Michaels, 1998, The Real Power of Real Options, Corporate Finance 158, January, pp. 13-20.

Majd, S., and R.S. Pindyck, Time to Build, Option Value, and Investment Decisions, Journal of Financial Economics 18, pp. 7-27.

McDonald, R., and D. Siegel, 1986, The Value of Waiting to Invest, The Quarterly Journal of Economics 101, November, pp. 707-27.

Myers, S.C., and S. Majd, 1990, Abandonment Value and Project Life, Advances in Futures and Options Research 4, pp. 1-21.

Siegel, D., J. Smith, and J. Paddock, 1987, Valuing Offshore Oil Properties with Option Pricing Models, Midland Journal of Corporate Finance, 5, pp. 22-30.

Trigeogis, Lenos, 1996, Real Options: Managerial Flexibility and Strategy in Resource Allocation, (The MIT Press, Cambridge, MA).

Trigeorgis, L., 1996, Interactions Among Multiple Real Options, Chapter 7 in Real Options: Managerial Flexibility and Strategy in Resource Allocation, (The MIT Press, Cambridge, MA).

Lattices and Real Options
"Using Real Options Software to Value Complex Options," by Jonathan Mun, Financial Engineering News ---

Real options are crucial in

* Identifying different corporate investment decision pathways or projects that management can navigate given the highly uncertain business conditions;
* Valuing each of the strategic decision pathway and what it represents in terms of financial viability and feasibility; * Prioritizing these pathways or projects based on a series of qualitative and quantitative metrics;
* Optimizing the value of your strategic investment decisions by evaluating different decision paths under certain conditions or using a different sequence of pathways can lead to the optimal strategy;
* Timing the effective execution of your investments and finding the optimal trigger values and cost or revenue drivers; and
* Managing existing or developing new optionalities and strategic decision pathways for future opportunities.

In financial options analysis, there are multiple methodologies and approaches used to calculate an option's value. These range from using closed-form equations like the Black-Scholes model and its modifications, Monte Carlo path-dependent simulation methods, lattices (for example, binomial, trinomial, quadranomial and multinomial trees), variance reduction and other numerical techniques, to using partial-differential equations, and so forth. However, in real options analysis, the mainstream methods that are most widely used are the closed-form solutions, partial-differential equations, and the binomial lattice trees.

The real options approach incorporates a learning model, such that management makes better and more informed strategic decisions when some levels of uncertainty are resolved through the passage of time. The discounted cash flow analysis assumes a static investment decision, and assumes that strategic decisions are made initially with no recourse to choose other pathways or options in the future. To create a good analogy of real options, visualize it as a strategic road map of long and winding roads with multiple perilous turns and branches along the way. Imagine the intrinsic and extrinsic value of having such a road map when navigating through unfamiliar territory, as well as having road signs at every turn to guide you in making the best and most informed driving decisions. This is the essence of real options.

Approaches in Solving Real Options Problems

Continued in article

Bob Jensen's threads on options valuation are at

Dissertation and Working Paper Links ---


I) Dissertations (Doctoral and M.Sc.) and Chapters/Papers from the Dissertations












II) Special Contributions







III) Working Papers







VI) Abstracts from Dissertations



Also see Bob Jensen's  Threads on Return on Investment (ROI)

Bob Jensen's Threads are at 

Bob Jensen's Homepage is at