Real option - AbsoluteAstronomy.com

Real options valuation, also often termed Real options analysis, (ROV or ROA) applies option

Option (finance)

In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

valuation techniques

Valuation of options

In finance, a price is paid or received for purchasing or selling options. This price can be split into two components.These are:* Intrinsic Value* Time Value-Intrinsic Value:...

to capital budgeting

Capital budgeting

Capital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing...

decisions. A real option itself, is the right — but not the obligation — to undertake some business decision; typically the option to make, abandon, expand, or contract 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 call

Call option

A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...

or put option

Put option

A put or put option is a contract between two parties to exchange an asset, the underlying, at a specified price, the strike, by a predetermined date, the expiry or maturity...

, respectively.

Real Options, as a discipline, extends from its application in Corporate Finance

Corporate finance

Corporate finance is the area of finance dealing with monetary decisions that business enterprises make and the tools and analysis used to make these decisions. The primary goal of corporate finance is to maximize shareholder value while managing the firm's financial risks...

, to decision making under uncertainty in general, adapting the techniques developed for financial options

Option (finance)

to "real-life" decisions. For example, R&D managers can use Real Options Valuation 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 to attend graduate school

Graduate school

A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate degree...

. 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.

Comparison with standard techniques

ROV is often contrasted with more standard techniques of capital budgeting

Capital budgeting

, such as discounted cash flow

Discounted cash flow

In finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...

(DCF) analysis / net present value

Net present value

In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...

(NPV).

Using a DCF model, only the most likely or representative outcomes are modelled, and the "flexibility" available to management is "ignored"; see Valuing flexibility under Corporate finance
Corporate finance
Corporate finance is the area of finance dealing with monetary decisions that business enterprises make and the tools and analysis used to make these decisions. The primary goal of corporate finance is to maximize shareholder value while managing the firm's financial risks...

. The NPV framework (implicitly) assumes that management is "passive" with regard to their Capital Investment once committed. Analysts usually account for this uncertainty by adjusting the discount rate (e.g. by increasing the cost of capital
Cost of capital
The cost of capital is a term used in the field of financial investment to refer to the cost of a company's funds , or, from an investor's point of view "the shareholder's required return on a portfolio of all the company's existing securities"...

) or the cash flows (using certainty equivalents, or applying (subjective) "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.
By contrast, ROV assumes that management is "active" and can modify the project as necessary. ROV models consider "all" future outcomes and management's response to these contingent scenarios. Because management responds to each outcome - i.e. the options are exercised
Exercise (options)
The owner of an option contract may exercise it, indicating that the financial transaction specified by the contract is to be enacted immediately between the two parties, and the contract itself is terminated...

- the possibility of a (large) negative outcome is reduced (or even eliminated), and /or greater profit is achieved. Risk is therefore reduced or "eliminated" under ROV, and uncertainty is accounted for using the techniques applied to financial options
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

. Here the approach is to risk-adjust the probabilities - as opposed to the discount rate, as for NPV - and the cash flow
Cash flow
Cash flow is the movement of money into or out of a business, project, or financial product. It is usually measured during a specified, finite period of time. Measurement of cash flow can be used for calculating other parameters that give information on a company's value and situation.Cash flow...

s can then be discounted at the risk-free rate. This technique is known as the certainty-equivalent or martingale approach, and uses a Risk-neutral measure
Risk-neutral measure
In mathematical finance, a risk-neutral measure, is a prototypical case of an equivalent martingale measure. It is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market a derivative's price is the discounted...

. 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. (As for financial options

Option (finance)

higher volatility of the underlying

Volatility (finance)

In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...

leads to higher value).

Valuation

From the above it is clear that there is an analog between the modelling of real options and financial options

Option (finance)

:
However, ROV is distinguished from these 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 ROV technically more challenging than its alternatives. When valuing the real option, the analyst must consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply.

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. The specific application, though, is as follows:

The option's underlying
Underlying
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 derivative depend on the value of this underlying...

is the project in question - it is modelled in terms of:
- spot price
  Spot price
  The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate settlement . Spot settlement is normally one or two business days from trade date...
  
  : the starting or current value
  Valuation (finance)
  In finance, valuation is the process of estimating what something is worth. Items that are usually valued are a financial asset or liability. Valuations can be done on assets or on liabilities...
  
  of the project is required: this is usually based on management's "best guess" as to the gross value of the project's cash flow
  Cash flow
  Cash flow is the movement of money into or out of a business, project, or financial product. It is usually measured during a specified, finite period of time. Measurement of cash flow can be used for calculating other parameters that give information on a company's value and situation.Cash flow...
  
  s and resultant NPV
  Net present value
  In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
  
  ;
- volatility
  Volatility (finance)
  In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
  
  : uncertainty as to the change in value over time is required:
  - the volatility in project value is generally used, usually derived via monte carlo simulation
    Monte Carlo methods in finance
    Monte Carlo methods are used in finance and mathematical finance to value and analyze instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining their average value over the range of resultant outcomes. This is usually done...
    
    ; sometimes the volatility of the first period's cash flows are preferred;
  - project NPV is often difficult to estimate, and some analysts therefore substitute a listed security as a proxy
    Proxy (statistics)
    In statistics, a proxy variable is something that is probably not in itself of any great interest, but from which a variable of interest can be obtained...
    
    , using either the volatility of the price of the security (historical volatility), or, if options exist on this security, their implied volatility
    Implied volatility
    In financial mathematics, the implied volatility of an option contract is the volatility of the price of the underlying security that is implied by the market price of the option based on an option pricing model. In other words, it is the volatility that, when used in a particular pricing model,...
    
    .

See further under Corporate finance
Corporate finance
Corporate finance is the area of finance dealing with monetary decisions that business enterprises make and the tools and analysis used to make these decisions. The primary goal of corporate finance is to maximize shareholder value while managing the firm's financial risks...

for a discussion relating to the estimation of NPV and project volatility.

Option characteristics:
- Strike price
  Strike price
  In options, the strike price is a key variable in a derivatives contract between two parties. Where the contract requires delivery of the underlying instrument, the trade will be at the strike price, regardless of the spot price of the underlying instrument at that time.Formally, the strike...
  
  : this corresponds to the investment outlays, typically the prospective costs of the project. In general, management would proceed (i.e. the option would be in the money
  In the Money
  In the Money is a comedy film starring The Bowery Boys. The film was released on February 16, 1958 by Allied Artists Pictures and is the forty-eighth and final film in the series. It was directed by William Beaudine and written by Al Martin and Elwood Ullman.-Plot summary:Sach is hired to take...
  
  ) given that the present value
  Present value
  Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...
  
  of expected cash flows exceeds this amount;
- Option term
  Expiration (options)
  For an option contract, expiration is the date on which the contract expires. The option holder must elect to exercise the option or allow it to expire worthless.Typically, option contracts expire according to a pre-determined calendar. For instance, for U.S...
  
  : the time during which management may decide to act, or not act, corresponds to the life of the option. Examples include the time to expiry of a patent
  Patent
  A patent is a form of intellectual property. It consists of a set of exclusive rights granted by a sovereign state to an inventor or their assignee for a limited period of time in exchange for the public disclosure of an invention....
  
  , or of the mineral rights
  Mineral rights
  - Mineral estate :Ownership of mineral rights is an estate in real property. Technically it is known as a mineral estate and often referred to as mineral rights...
  
  for a new mine. See Option time value
  Option time value
  In finance, the time value of an option is the premium a rational investor would pay over its current exercise value , based on its potential to increase in value before expiring. This probability is always greater than zero, thus an option is always worth more than its current exercise value...
  
  .
Option style
Option style
In finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American options. These options - as well as others where the...

. Management's ability to respond to changes in value is modeled at each decision point as a series of options:
- the option to contract the project (an American styled put option
  Put option
  A put or put option is a contract between two parties to exchange an asset, the underlying, at a specified price, the strike, by a predetermined date, the expiry or maturity...
  
  );
- the option to abandon the project (also an American put);
- the option to expand or extend the project (both American styled call option
  Call option
  A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...
  
  s);
- switching options, composite options or rainbow option
  Rainbow option
  Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. Rainbow options are usually calls or puts on the best or worst of n underlying assets, or options which...
  
  s which may also apply to the project.

Valuation methods

The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options

Valuation of options

In finance, a price is paid or received for purchasing or selling options. This price can be split into two components.These are:* Intrinsic Value* Time Value-Intrinsic Value:...

. 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.

The most commonly employed are Closed form
Closed form
-Maths:* Closed-form expression, a finitary expression* Closed differential form, a differential form \alpha with the property that d\alpha = 0-Poetry:* In poetry analysis, a type of poetry that exhibits regular structure, such as meter or a rhyming pattern;...

solutions—often modifications to Black Scholes—and binomial lattices
Binomial options pricing model
In finance, the binomial options pricing model provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. Essentially, the model uses a “discrete-time” model of the varying price over time of the underlying...

. The latter are probably more widely used due to their flexibility, particularly given that most real options are American styled, although cannot readily handle high dimensional problems.
Specialised Monte Carlo Methods
Monte Carlo methods in finance
Monte Carlo methods are used in finance and mathematical finance to value and analyze instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining their average value over the range of resultant outcomes. This is usually done...

have also been developed and are increasingly applied particularly to high dimensional problems, although for American styled real options, this application is somewhat more complex.
When the Real Option can be modelled using a partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

, then Finite difference methods for option pricing
Finite difference methods for option pricing
Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977....

are sometimes applied. Although many of the early ROV articles discussed this method, 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 practitioner

Practitioner

A practitioner is someone who engages in an occupation, profession, religion, or way of life.Practitioner may refer to:* Medical practitioner* Justice practitioner* Solitary practitioner, in Wicca and Paganism...

s, 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

Datar-Mathews Method for Real Option Valuation

The Datar-Mathews Method is a new method for Real options valuation. The DM Method can be understood as an extension of the net present value multi-scenario Monte Carlo model with an adjustment for risk-aversion and economic decision-making. The method uses information that arises naturally in a...

and the Fuzzy Pay-Off Method

Fuzzy Pay-Off Method for Real Option Valuation

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 pay-off distribution of a possible project...

Limitations

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

Organizational considerations

Real options are “particularly important for businesses with a few key characteristics”, and may be less relevant otherwise. At the same time the market in question must be one where "change is most evident", and the "source, trends and evolution" in product demand and supply, create the volatility and contingencies discussed above.

In overview:

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.
Management must understand options, be able to identify and create them, and appropriately exercise them. (This contrasts with business leaders focused on maintaining the status quo and / or near-term accounting earnings.)
The financial position of the business must be such that it has the ability to fund the project as required (i.e. issue shares, absorb further debt and / or use internally generated cash flow); see Financial statement analysis
Financial statement analysis
Financial statement analysis is the process of understanding the risk and profitability of a firm through analysis of reported financial information, particularly annual and quarterly reports....

. Management must also have appropriate access to this capital.

Technical considerations

Limitations as to the use of these models arise due to the contrast between Real Options and financial options

Option (finance)

, for which these were originally developed. The main difference is that the underlying

Underlying

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 derivative depend on the value of this underlying...

is often not tradeable - 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

Market liquidity

In business, economics or investment, market liquidity is an asset's ability to be sold without causing a significant movement in the price and with minimum loss of value...

.

The difficulties:

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
Spot price
The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate settlement . Spot settlement is normally one or two business days from trade date...

) and volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...

(further complicated by uncertainty as to management's actions in the future).
It is often difficult to capture the rules relating to exercise, and consequent actions by management: Some real options are proprietary (owned or exercisable by a single individual or a company) while others are shared (can be exercised by many parties). Further, a project may have a portfolio of embedded real options, some of which may be mutually exclusive.
Theoretical difficulties, which are more serious, may also arise.

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
Arbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

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
Discount rate
The discount rate can mean*an interest rate a central bank charges depository institutions that borrow reserves from it, for example for the use of the Federal Reserve's discount window....

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:

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.
Specific exercise rules can often be accommodated by coding these in a bespoke binomial tree
Binomial options pricing model
In finance, the binomial options pricing model provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. Essentially, the model uses a “discrete-time” model of the varying price over time of the underlying...

; see:.
The theoretical issues:

To use standard option pricing models here, despite the difficulties relating to rational pricing, practitioners adopt the "fiction"
Legal fiction
A legal fiction is a fact assumed or created by courts which is then used in order to apply a legal rule which was not necessarily designed to be used in that way...

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, interestingly, a similar fiction in fact underpins standard NPV / DCF valuation (and using simulation as above). See: and.
To address the fact that changing characteristics invalidate the use of a constant discount rate, some practitioners use the "replicating portfolio approach", as opposed to Risk neutral valuation, and modify their models correspondingly. Under this approach, we "replicate" the cash flows on the option by holding a risk free bond and the underlying in the correct proportions. Then, since the value of the option and the portfolio will be identical in the future, they may be equated today, and 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

Stewart Myers

Stewart Clay Myers is the Robert C. Merton Professor of Financial Economics at the MIT Sloan School of Management. He is notable for his work on capital structure and innovations in capital budgeting and valuation, and has had a "remarkable influence" on both the theory and practice of corporate...

of the MIT Sloan School of Management

MIT Sloan School of Management

The MIT Sloan School of Management is the business school of the Massachusetts Institute of Technology, in Cambridge, Massachusetts....

in 1977. It is interesting to note though, that in 1930, Irving Fisher

Irving Fisher

Irving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...

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

Option (finance)

, 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

Lenos Trigeorgis

Lenos Trigeorgis is the Bank of Cyprus Chair Professor of Finance in the School of Economics and Management, University of Cyprus. He is considered a leading authority on capital budgeting and strategy, having pioneered the field of real options...

(University of Cyprus

University of Cyprus

The University of Cyprus is a public coeducational university established by the Republic of Cyprus in 1989. It admitted its first students in 1992 and has currently approximately 6000 students .-History:...

) 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

Eduardo Schwartz

Eduardo Saul Schwartz is a professor of finance at the Anderson School of Management, University of California, Los Angeles, where he holds the California Chair in Real Estate & Land Economics...

and Michael Brennan

Michael Brennan (finance)

Michael J. Brennan is emeritus professor of finance at the UCLA Anderson School of Management. Brennan co-designed the Brennan-Schwartz interest rate model and was a pioneer of real options theory...

(UCLA Anderson). An academic conference on real options is organized yearly (Annual International Conference on Real Options

Annual International Conference on Real Options

The Annual International Conference on Real Options: Theory Meets Practice is a yearly conference organized by the Real Options Group in cooperation with various top universities...

).

Amongst others, the concept was "popularized" by Michael J. Mauboussin

Michael Mauboussin

Michael J. Mauboussin, Chief Investment Strategist at Legg-Mason Capital Management Inc and Adjunct Professor of Finance at the Columbia Business School, is regarded as one of the world’s experts in behavioural finance, and is widely read as an author and as an analyst.Prior to joining Legg-Mason...

, then chief U.S. investment strategist for Credit Suisse First Boston

Credit Suisse First Boston

Credit Suisse First Boston was the former name of the banking firm Credit Suisse.-History:In 1978, Credit Suisse and First Boston Corporation formed a London-based 50-50 investment banking joint venture called the Financière Crédit Suisse-First Boston...

. He uses real options to explain the gap between how the stock market prices some businesses and the "intrinsic value

Intrinsic value

Intrinsic value can refer to:*Intrinsic value , of an option or stock.*Intrinsic value , of a coin.*Intrinsic value , in ethics and philosophy.*Intrinsic value , in philosophy....

" for those businesses. Trigeorgis also has broadened exposure to real options through layman articles in publications such as The Wall Street Journal

The Wall Street Journal

The Wall Street Journal is an American English-language international daily newspaper. It is published in New York City by Dow Jones & Company, a division of News Corporation, along with the Asian and European editions of the Journal....

. This popularization is such that ROV is now a standard offering in postgraduate finance degrees

Master of Finance

A Master of Finance is a Master's degree designed to prepare graduates for careers in financial analysis, investment management and corporate finance. An alternate degree title is Master in Finance or Master of Science in Finance...

, 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

Conceptual framework

A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to an idea or thought. For example, the philosopher Isaiah Berlin used the "hedgehogs" versus "foxes" approach; a "hedgehog" might approach the world in terms of a single organizing...

. The idea of treating strategic investments as options was popularized by Timothy Luehrman

Timothy Luehrman

Timothy A. Luehrman is a Finance academic at Harvard Business School. He is best known for his work on valuation and real options; specifically, he conceived the idea of treating business strategy as a series of options, and his papers here are widely quoted....

in two HBR

Harvard Business Review

Harvard Business Review is a general management magazine published since 1922 by Harvard Business School Publishing, owned by the Harvard Business School. A monthly research-based magazine written for business practitioners, it claims a high ranking business readership among academics, executives,...

articles: "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").

Comparison with standard techniques

Valuation

Valuation inputs

Valuation methods

Limitations

Organizational considerations

Technical considerations

History

See also

Theory

Journals

Applications