Real options valuation, also often termed real options analysis,
[Adam Borison (]Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...
)
''Real Options Analysis: Where are the Emperor's Clothes?''
(ROV or ROA) applies
option valuation techniques to
capital budgeting
Capital budgeting in corporate finance is the planning process used to determine whether an organization's long term capital investments such as new machinery, replacement of machinery, new plants, new products, and research development project ...
decisions.
[Campbell, R. Harvey]
''Identifying real options''
Duke University, 2002. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project.
For example, 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.
[Nijssen, E. (2014)]
Routelegde, 2014.
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. A further distinction is that option holders here, i.e. management, can directly influence the value of the option's
underlying
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be use ...
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.
Real options analysis, as a discipline, extends from its application in
corporate finance
Corporate finance is the area of finance that deals with the sources of funding, the capital structure of corporations, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and anal ...
, 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. Non business examples might be evaluating the cost of
cryptocurrency
A cryptocurrency, crypto-currency, or crypto is a digital currency designed to work as a medium of exchange through a computer network that is not reliant on any central authority, such as a government or bank, to uphold or maintain it. It i ...
mining machines, or the decision to join the work force, or rather, to forgo several years of income to attend
graduate school
Postgraduate or graduate education refers to Academic degree, academic or professional degrees, certificates, diplomas, or other qualifications pursued by higher education, post-secondary students who have earned an Undergraduate education, un ...
. 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
In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessmen ...
formulation.
[Justin Pettit]
''Applications in Real Options and Value-based Strategy''
Ch.4. in Trigeorgis (1996)[Joanne Sammer]
Thinking in Real (Options) Time
businessfinancemag.com[David Shimko (2009)]
Real Options: Opportunity from Risk
archived 2010-04-05. This extension of real options to real-world projects often requires customized
decision support system
A decision support system (DSS) is an information system that supports business or organizational decision-making activities. DSSs serve the management, operations and planning levels of an organization (usually mid and higher management) and h ...
s, because otherwise the complex compound real options will become too intractable to handle.
Types of real options
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. In all cases, any (non-recoverable) upfront expenditure related to this flexibility is the
option premium
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the imple ...
. Real options are also commonly applied to
stock valuation
In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit fr ...
- see - 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.
*Option to expand: Here the project is built with capacity in excess of the expected level of output so that it can produce at higher rate if needed. Management then has the option (but not the obligation) to expand – i.e.
exercise the option – should conditions turn out to be favourable. A project with the option to expand will cost more to establish, the excess being the
option premium
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the imple ...
, but is worth more than the same without the possibility of expansion. This is equivalent to a
call option
In finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an ...
.
*Option to contract : The project is engineered such that output can be contracted in future should conditions turn out to be unfavourable. Forgoing these future expenditures constitutes
option exercise. This is the equivalent to a
put option
In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the ''underlying''), at a specified price (the ''strike''), by (or at) a s ...
, and again, the excess upfront expenditure is the
option premium
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the imple ...
.
*Option to expand or contract: Here the project is designed such that its operation can be dynamically turned on and off. Management may shut down part or all of the operation when conditions are unfavorable (a put option), and may restart operations when conditions improve (a call option). A
flexible manufacturing system
A flexible manufacturing system (FMS) is a manufacturing system in which there is some amount of flexibility that allows the system to react in case of changes, whether predicted or unpredicted.
This flexibility is generally considered to fall ...
(FMS) is a good example of this type of option. This option is also known as a
Switching option
Real options valuation, also often termed real options analysis,Adam Borison ( Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?''
(ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campb ...
.
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.
*Initiation or deferment options: Here management has flexibility as to when to start a project. For example, in
natural resource
Natural resources are resources that are drawn from nature and used with few modifications. This includes the sources of valued characteristics such as commercial and industrial use, aesthetic value, scientific interest and cultural value. O ...
exploration a firm can delay mining a deposit until market conditions are favorable. This constitutes an
American styled call option
In finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an ...
.
*Delay option with a product patent: A firm with a
patent
A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an enabling disclosure of the invention."A p ...
right on a product has a right to develop and market the product exclusively until the expiration of the patent. The firm will market and develop the product only if the present value of the expected cash flows from the product sales exceeds the cost of development. If this does not occur, the firm can shelve the patent and not incur any further costs.
*Option to abandon: Management may have the option to cease a project during its life, and, possibly, to realise its
salvage value
''Residual value'' is one of the constituents of a leasing calculus or operation. It describes the future value of a good in terms of absolute value in monetary terms and it is sometimes abbreviated into a percentage of the initial price when the i ...
. Here, when the present value of the remaining cash flows falls below the liquidation value, the asset may be sold, and this act is effectively the exercising of a
put option
In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the ''underlying''), at a specified price (the ''strike''), by (or at) a s ...
. This option is also known as a
Termination option
Real options valuation, also often termed real options analysis,Adam Borison ( Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?''
(ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campb ...
. Abandonment options are
American styled.
*Sequencing options: This option is related to the initiation option above, although entails flexibility as to the timing of more than one inter-related projects: the analysis here is as to whether it is advantageous to implement these
sequentially
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called t ...
or
in parallel. Here, observing the outcomes relating to the first project, the firm can resolve some of the uncertainty relating to the venture overall. Once resolved, management has the option to proceed or not with the development of the other projects. If taken in parallel, management would have already spent the resources and the value of the option not to spend them is lost. The sequencing of projects is an important issue in
corporate strategy
In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessment ...
. Related here is also the notion of Intraproject vs. Interproject options.
*Option to prototype: New energy generation and storage systems are continuously being developed due to climate change, resource scarcity, and environmental laws. Some systems are incremental innovations of existing systems while others are radical innovations. Radical innovation systems are risky investments due to their relevant technical and economic uncertainties. Prototyping can hedge these risks by spending a fraction of the cost of a full-scale system and in return receiving economic and technical information regarding the system. In economic terms, prototyping is an option to hedge risk coming at a cost that needs to be properly assessed.
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.
*Output mix options: The option to produce different outputs from the same facility is known as an output mix option or product flexibility. These options are particularly valuable in industries where demand is volatile or where quantities demanded in total for a particular good are typically low, and management would wish to change to a different product quickly if required.
*Input mix options: An input mix option – process flexibility – allows management to use different inputs to produce the same output as appropriate. For example, a farmer will value the option to switch between various feed sources, preferring to use the cheapest acceptable alternative. An
electric utility
An electric utility is a company in the electric power industry (often a public utility) that engages in electricity generation and distribution of electricity for sale generally in a regulated market. The electrical utility industry is a major pr ...
, for example, may have the option to switch between various fuel sources to produce electricity, and therefore a flexible plant, although more expensive may actually be more valuable.
*Operating scale options: Management may have the option to change the output rate per unit of time or to change the total length of production run time, for example in response to market conditions. These options are also known as
Intensity options.
Valuation
Given the above, it is clear that there is an
analogy
Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject ( ...
between real options and
financial options,
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.
Applicability of standard techniques
ROV is often contrasted with more standard techniques of
capital budgeting
Capital budgeting in corporate finance is the planning process used to determine whether an organization's long term capital investments such as new machinery, replacement of machinery, new plants, new products, and research development project ...
, such as
discounted cash flow
The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money.
Discounted cash flow analysis is widely used in investment finance, real estate devel ...
(DCF) analysis /
net present value
The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ...
(NPV).
Under this "standard" NPV approach, future expected cash flows are
present value
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
d under the
empirical probability measure at a discount rate that reflects the embedded risk in the project; see
CAPM CAPM may refer to:
* Capital asset pricing model, a fundamental model in finance
* Certified Associate in Project Management, an entry-level credential for project managers
{{Disambig ...
,
APT
Apt. is an abbreviation for apartment.
Apt may also refer to:
Places
* Apt Cathedral, a former cathedral, and national monument of France, in the town of Apt in Provence
* Apt, Vaucluse, a commune of the Vaucluse département of France
* A ...
,
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 .
The NPV framework (implicitly) assumes that management is "passive" with regard to their
Capital Investment
Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort.
In finance, the purpose of investing is ...
once committed.
Some analysts account for this uncertainty by
(i) adjusting the discount rate, e.g. by increasing the
cost of capital
In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new ...
,
or (ii) adjusting the cash flows, e.g. using
certainty equivalent
A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky Rate of retur ...
s,
or (iii) applying (subjective) "haircuts" to the forecast numbers,
or (iv) via probability-weighting these as in
rNPV
In finance, rNPV ("risk-adjusted net present value") or eNPV ("expected NPV") is a method to value risky future cash flows.
rNPV is the standard valuation method in the drug development industry,
where sufficient data exists to estimate success ...
.
[Aswath Damodaran]
Risk Adjusted Value
Ch 5 in ''Strategic Risk Taking: A Framework for Risk Management''. Wharton School Publishing
Wharton School Publishing was a publishing house, a division of The Wharton School and Pearson, the world's largest education publishing and technology company. The imprint brought together a variety of business educators and corporate executives ...
, 2007.
[See: §32 "Certainty Equivalent Approach" & §165 "Risk Adjusted Discount Rate" in: ]
[Aswath Damodaran:]
Valuing Firms in Distress
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.
[Dan Latimore]
''Calculating value during uncertainty''
IBM Institute for Business Value
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.
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
In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or ''equivalent martingale measure'') is a probability measure such that each share price is exactly equal to the discounted expectation of the share price und ...
. 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 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.) 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.
Options based valuation
Although there is much similarity between the modelling of real options and
financial options,
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.
[Jenifer Piesse and Alexander Van de Putte. (2004)]
"Volatility estimation in Real Options"
8th Annual International Conference on Real Options It is the combined effect of these that makes ROV technically more challenging than its alternatives.
When valuing the real option, the analyst must therefore consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply. Conceptually, valuing a real option looks at the premium between inflows and outlays for a particular project. Inputs to the value of a real option (time, discount rates, volatility, cash inflows and outflows) are each affected by the terms of business, and external environmental factors that a project exists in. Terms of business as information regarding ownership, data collection costs, and patents, are formed in relation to political, environmental, socio-cultural, technological, environmental and legal factors that affect an industry. Just as terms of business are affected by external environmental factors, these same circumstances affect the volatility of returns, as well as the discount rate (as firm or project specific risk). Furthermore, the external environmental influences that affect an industry affect projections on expected inflows and outlays.
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
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be use ...
is the project in question – it is modelled in terms of:
**
Spot price
In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the ...
: the starting or current
value
Value or values may refer to:
Ethics and social
* Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them
** Values (Western philosophy) expands the notion of value beyo ...
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
A cash flow is a real or virtual movement of money:
*a cash flow in its narrow sense is a payment (in a currency), especially from one central bank account to another; the term 'cash flow' is mostly used to describe payments that are expected ...
s and resultant
NPV;
**
Volatility: a measure for 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, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determini ...
;
sometimes the volatility of the first period's cash flows are preferred;
see
further
Further or Furthur may refer to:
* ''Furthur'' (bus), the Merry Pranksters' psychedelic bus
* Further (band), a 1990s American indie rock band
* Furthur (band), a band formed in 2009 by Bob Weir and Phil Lesh
* ''Further'' (The Chemical Brothers a ...
under
Corporate finance
Corporate finance is the area of finance that deals with the sources of funding, the capital structure of corporations, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and anal ...
for a discussion relating to the estimation of NPV and project volatility.
*** some analysts substitute a
listed security as a
proxy
Proxy may refer to:
* Proxy or agent (law), a substitute authorized to act for another entity or a document which authorizes the agent so to act
* Proxy (climate), a measured variable used to infer the value of a variable of interest in climate ...
, using either its price volatility (
historical volatility), or, if options exist on this security, their
implied volatility In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equ ...
.
**
Dividend
A dividend is a distribution of profits by a corporation to its shareholders. When a corporation earns a profit or surplus, it is able to pay a portion of the profit as a dividend to shareholders. Any amount not distributed is taken to be re-in ...
s generated by the underlying asset: As part of a project, the dividend equates to any income which could be derived from the real assets and paid to the owner. These reduce the appreciation of the asset.
* Option characteristics:
**
Strike price
In finance, the strike price (or exercise price) of an option is a fixed price at which the owner of the option can buy (in the case of a call), or sell (in the case of a put), the underlying security or commodity. The strike price may be set b ...
: this corresponds to any (non-recoverable) investment outlays, typically the prospective costs of the project. In general, management would proceed (i.e. the option would be
in the money
In finance, moneyness is the relative position of the current price (or future price) of an underlying asset (e.g., a stock) with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a thr ...
) given that the
present value
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
of expected cash flows exceeds this amount;
**
Option term: the time during which management may decide to act, or not act, corresponds to the life of the option. As above, examples include the time to expiry of a
patent
A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an enabling disclosure of the invention."A p ...
, or of the
mineral rights
Mineral rights are property rights to exploit an area for the minerals it harbors. Mineral rights can be separate from property ownership (see Split estate). Mineral rights can refer to sedentary minerals that do not move below the Earth's surfac ...
for a new mine. See
Option time value In finance, the time value (TV) (''extrinsic'' or ''instrumental'' value) of an option is the premium a rational investor would pay over its ''current'' exercise value ( intrinsic value), based on the probability it will increase in value before ex ...
. Note though that given the flexibility related to timing
as described, caution must be applied here.
**
Option style In finance, the style or family of an option is 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 (style) options. These options ...
and
option exercise. Management's ability to respond to changes in value is modeled at each decision point as a series of options, as above these may comprise, i.a.:
*** the
option to contract the project (an
American styled put option
In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the ''underlying''), at a specified price (the ''strike''), by (or at) a s ...
);
*** the
option to abandon the project (also an American put);
*** the
option to expand
Real options valuation, also often termed real options analysis,Adam Borison (Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?''
(ROV or ROA) applies option (finance), option Valuation of options, valuation techniques ...
or extend the project (both
American styled call option
In finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an ...
s);
***
switching option
Real options valuation, also often termed real options analysis,Adam Borison ( Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?''
(ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campb ...
s or
composite option
Composite or compositing may refer to:
Materials
* Composite material, a material that is made from several different substances
** Metal matrix composite, composed of metal and other parts
** Cermet, a composite of ceramic and metallic materials
...
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.
Note though that, in general, while most "real" problems allow for
American style
This is a list of dance terms that are not names of dances or types of dances. See List of dances and List of dance style categories for those.
This glossary lists terms used in various types of ballroom partner dances, leaving out terms of high ...
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
A trade-off (or tradeoff) is a situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and anot ...
between these considerations; see . The model must also be flexible enough to allow for the relevant decision rule to be coded appropriately at each decision point.
*
Closed form,
Black–Scholes-like solutions are sometimes employed.
These are applicable only for
European styled options or perpetual American options. Note that this application of Black–Scholes assumes constant — i.e.
deterministic
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...
— costs: in cases where the project's costs, like its revenue, are also assumed stochastic, then
Margrabe's formula
In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (PhD Chicago) in 1978. Margrabe's paper has been ...
can (should) be applied instead,
[See Ch. 23, Sec. 5, in: Frank Reilly, Keith Brown (2011). "Investment Analysis and Portfolio Management." (10th Edition). South-Western College Pub. ] here valuing the option to "exchange" expenses for revenue. (Relatedly, where the project is exposed to two (or more) uncertainties — e.g. for natural resources, price and quantity — some analysts attempt to use an overall volatility; this, though, is more correctly treated as a
rainbow option 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.
The name of ''rainbow'' comes from Rubinstein (1991), ...
,
typically valued using simulation as below.)
* The most commonly employed methods are
binomial lattices.
These are more widely used given that most real options are
American styled. Additionally, and particularly,
lattice-based models allow for flexibility as to exercise, where the relevant, and differing, rules may be encoded at each node.
Note that lattices cannot readily handle high-dimensional problems; treating the project's costs as stochastic would add (at least) one dimension to the lattice, increasing the number of ending-nodes
by the square (the exponent here, corresponding to the number of sources of uncertainty).
*
Specialised Monte Carlo Methods have also been developed and are increasingly, and especially, applied to
high-dimensional
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
problems.
[Marco Dias]
''Real Options with Monte Carlo Simulation''
Note that for American styled real options, this application is somewhat more complex; although recent research combines a
least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
approach with simulation, allowing for the valuation of real options which are both multidimensional and American styled; see .
* When the Real Option can be modelled using a
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
, then
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.
In general, finite differ ...
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 may refer to:
*Health practitioner
*Justice and public safety practitioner
* Legal practitioner
* Medical practitioner
*Mental health professional or practitioner
*Theatre practitioner
Spiritual Practitioner
* Solitary practitioner ...
s, have been developed for real option valuation.
These typically use
cash-flow
A cash flow is a real or virtual movement of money:
*a cash flow in its narrow sense is a payment (in a currency), especially from one central bank account to another; the term 'cash flow' is mostly used to describe payments that are expected ...
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,
fuzzy pay-off method, the simulation with optimised exercise thresholds method.
Limitations
The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations.
[Ronald Fink]
Reality Check for Real Options
''CFO Magazine'', September, 2001 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"
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",
and may be less relevant otherwise.
In overview, it is important to consider the following in determining that the RO framework is applicable:
#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.
# Practically, the business must be positioned such that it has appropriate information flow, and opportunities to act. This will often be a
market leader
Market dominance describes when a firm can control markets. A dominant firm possesses the power to affect competition and influence market price. A firms' dominance is a measure of the power of a brand, product, service, or firm, relative to ...
and / or a firm enjoying
economies of scale
In microeconomics, economies of scale are the cost advantages that enterprises obtain due to their scale of operation, and are typically measured by the amount of output produced per unit of time. A decrease in cost per unit of output enables ...
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, and when, required (i.e. issue shares, absorb further debt and / or use internally generated cash flow); see
Financial statement analysis
Financial statement analysis (or just financial analysis) is the process of reviewing and analyzing a company's financial statements to make better economic decisions to earn income in future. These statements include the income statement, balanc ...
. Management must, correspondingly, have appropriate access to this capital.
# 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.
[Don M. Chance and Pamela P. Peterson (2002)]
Real Options and Investment Valuation
The Research Foundation of AIMR
The main difference is that the
underlying
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be use ...
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
In business, economics or investment, market liquidity is a market's feature whereby an individual or firm can quickly purchase or sell an asset without causing a drastic change in the asset's price. Liquidity involves the trade-off between the ...
. 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:
# 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
In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the ...
) and
volatility (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. 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.
[See Marco Dias]
Does Risk-Neutral Valuation Mean that Investors Are Risk-Neutral?
/ref>
::*Option pricing models are built on rational pricing
Rational pricing is the assumption in financial economics that asset prices - and hence asset pricing models - will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is use ...
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
In economics and finance, arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between the ...
arguments then allow for the option's price to be estimated today; see . (c) When hedging of this sort is possible, since delta hedging and risk neutral pricing are ''mathematically'' identical, then risk neutral valuation may be applied, as is the case with most option pricing models. (d) Under ROV however, the option and (usually) its underlying are clearly not traded, and forming a hedging portfolio would be difficult, if not impossible.
::*Standard option models: (a) Assume that the risk characteristics of the underlying do not change over the life of the option, usually expressed via a constant volatility assumption. (b) Hence a standard, risk free rate may be applied as the discount rate at each decision point, allowing for risk neutral valuation. Under ROV, however: (a) managements' actions actually change the risk characteristics of the project in question, and hence (b) the Required rate of return
The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money.
Discounted cash flow analysis is widely used in investment finance, real estate devel ...
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.
# Also as above
''As Above...'' was an album released in 1982 by Þeyr, an Icelandic new wave and rock group. It was issued through the Shout record label on a 12" vinyl record.
Consisting of 12 tracks, ''As above...'' contained English versions of the band' ...
, specific exercise rules can often be accommodated by coding these in a bespoke binomial tree
In computer science, a binomial heap is a data structure that acts as a priority queue but also allows pairs of heaps to be merged.
It is important as an implementation of the mergeable heap abstract data type (also called meldable heap), whic ...
; see:.
# 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: and.
::*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. 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: .)
History
Whereas business managers have been making capital investment decisions for centuries, the term "real option" is relatively new, and was coined by Professor Stewart Myers of the MIT Sloan School of Management
The MIT Sloan School of Management (MIT Sloan or Sloan) is the business school of the Massachusetts Institute of Technology, a private university in Cambridge, Massachusetts.
MIT Sloan offers bachelor's, master's, and doctoral degree programs, ...
in 1977. In 1930, Irving Fisher
Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, eugenicist and progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt def ...
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
Eduardo Saul Schwartz (born 1940) is a professor of finance at SFU's Beedie School of Business, where he holds the Ryan Beedie Chair in Finance. He is also a Distinguished Research Professor at the University of California, Los Angeles. He is know ...
Graham Davis
Gonzalo Cortazar
Han Smit
Avinash Dixit
Avinash Kamalakar Dixit (born 6 August 1944) is an Indian-American economist. He is the John J. F. Sherrerd '52 University Professor of Economics Emeritus at Princeton University, and has been Distinguished Adjunct Professor of Economics at Lin ...
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 Michael J. Mauboussin (born February 1964) heads consilient research at Morgan Stanley division Morgan Stanley Investment Management's Counterpoint Global, an open-end mutual fund. Previously, he was director of research at BlueMountain Capital and ...
, then chief U.S. investment strategist for Credit Suisse First Boston
Credit Suisse First Boston (also known as CSFB and CS First Boston) is the investment banking affiliate of Credit Suisse headquartered in New York.
The company was created by the merger of First Boston Corporation and Credit Suisse Group in 1988 ...
.[Michael J. Mauboussin, Credit Suisse First Boston, 1999]
''Get Real: Using Real Options in Security Analysis''
/ref> 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
''The Wall Street Journal'' is an American business-focused, international daily newspaper based in New York City, with international editions also available in Chinese and Japanese. The ''Journal'', along with its Asian editions, is published ...
.[Lenos Trigeorgis, Rainer Brosch and Han Smit]
''Stay Loose''
copyright 2010 Dow Jones & Company
Dow Jones & Company, Inc. is an American publishing firm owned by News Corp and led by CEO Almar Latour.
The company publishes ''The Wall Street Journal'', ''Barron's'', ''MarketWatch'', ''Mansion Global'', ''Financial News'' and ''Private Equ ...
. This popularization is such that ROV is now a standard offering in postgraduate finance degrees, and often, even in MBA
A Master of Business Administration (MBA; also Master's in Business Administration) is a postgraduate degree focused on business administration. The core courses in an MBA program cover various areas of business administration such as accounti ...
curricula at many Business Schools
A business school is a university-level institution that confers degrees in business administration or management. A business school may also be referred to as school of management, management school, school of business administration, o ...
.
Recently, real options have been employed in business strategy
In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessmen ...
, both for valuation purposes and as a conceptual framework
A conceptual framework is an analytical tool with several variations and contexts. It can be applied in different categories of work where an overall picture is needed. It is used to make conceptual distinctions and organize ideas. Strong conceptu ...
. The idea of treating strategic investments as options was popularized by Timothy Luehrman Timothy A. Luehrman is a finance academic, formerly a senior lecturer 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 option (f ...
in two HBR articles:[Timothy Luehrman: "Investment Opportunities as Real Options: Getting Started on the Numbers". '']Harvard Business Review
''Harvard Business Review'' (''HBR'') is a general management magazine published by Harvard Business Publishing, a wholly owned subsidiary of Harvard University. ''HBR'' is published six times a year and is headquartered in Brighton, Massach ...
'' 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. "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.[Timothy A. Luehrman and William A. Teichner]
"Arundel Partners: The Sequel Project."
''Harvard Business School Publishing
Harvard Business Publishing was founded in 1994 as a not-for-profit, wholly owned subsidiary of Harvard University (distinct from Harvard University Press), with a focus on improving business management practices. The company consists of three ...
'' case no. 9-292-140 (1992) Reflecting the "mainstreaming" of ROV, Professor Robert C. Merton
Robert Cox Merton (born July 31, 1944) is an American economist, Nobel Memorial Prize in Economic Sciences laureate, and professor at the MIT Sloan School of Management, known for his pioneering contributions to continuous-time finance, especia ...
discussed the essential points of Arundel in his Nobel Prize
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...
Lecture
A lecture (from Latin ''lēctūra'' “reading” ) is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical inform ...
in 1997.[Robert Merton, ]Nobel Lecture
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...
''Applications of Option-Pricing Theory: Twenty-Five Years Later''
Pages 107, 115; reprinted: ''American Economic Review
The ''American Economic Review'' is a monthly peer-reviewed academic journal published by the American Economic Association. First published in 1911, it is considered one of the most prestigious and highly distinguished journals in the field of ec ...
'', American Economic Association
The American Economic Association (AEA) is a learned society in the field of economics. It publishes several peer-reviewed journals acknowledged in business and academia. There are some 23,000 members.
History and Constitution
The AEA was esta ...
, vol. 88(3), pages 323–49, June. 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)
In the film industry, an option is a contractual agreement pertaining to film rights between a potential film producer (such as a movie studio, a production company, or an individual) and the author of source material, such as a book, play, or ...
.
See also
* Option contract
An option contract, or simply option, is defined as "a promise which meets the requirements for the formation of a contract and limits the promisor's power to revoke an offer". Option contracts are common in professional sports.
An option contrac ...
* Opportunity cost
In microeconomic theory, the opportunity cost of a particular activity is the value or benefit given up by engaging in that activity, relative to engaging in an alternative activity. More effective it means if you chose one activity (for example ...
* Monte Carlo methods in finance Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the dist ...
* Contingent claim valuation In finance, a contingent claim is a derivative whose future payoff depends on the value of another “underlying” asset,Dale F. Gray, Robert C. Merton and Zvi Bodie. (2007). Contingent Claims Approach to Measuring and Managing Sovereign Credit Ri ...
* Fuzzy pay-off method for real option valuation The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzz ...
* Datar–Mathews method for real option valuation The Datar–Mathews Method (DM Method) is a method for real options valuation. The method provides an easy way to determine the real option value of a project simply by using the average of positive outcomes for the project. The method can be unders ...
*
*
*
*
*
*Contingent value rights
In corporate finance,
Contingent Value Rights (CVR) are rights granted by an acquirer to a company’s shareholders, facilitating the transaction where some uncertainty is inherent.
CVRs may be separately tradeable securities; they are occasiona ...
References
Further reading
Standard texts:
*
*
*
*
*
*
*
*
*
Applications:
*
*
*
*
*
*Grenadier, Steven R. & Weiss, Allen M., 1997. "Investment in technological innovations: An option pricing approach," ''Journal of Financial Economics
The ''Journal of Financial Economics'' is a peer-reviewed academic journal published by Elsevier, covering the field of finance. It is considered to be one of the premier finance journals. According to the ''Journal Citation Reports'', the journa ...
'', Elsevier, vol. 44(3), pages 397–416, June.
*
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*
The Impact of Real Options in Agency Problems
G. Siller-Pagaza, G. Otalora, E. Cobas-Flores (2006).
*
*
*
External links
Theory
Intro to Real Option Valuation as a Modelling Problem
Mikael Collan
The Promise and Peril of Real Options
Prof. Aswath Damodaran
Aswath Damodaran (born 24 September 1957), is a Professor of Finance at the Stern School of Business at New York University (Kerschner Family Chair in Finance Education), where he teaches corporate finance and equity valuation.
Background
Know ...
, Stern School of Business
The New York University Leonard N. Stern School of Business (commonly referred to as NYU Stern, The Stern School of Business, or simply Stern) is the business school of New York University, a private research university based in New York City. I ...
Real Options Tutorial
Prof. Marco Dias, PUC-Rio
The Pontifical Catholic University of Rio de Janeiro ( pt, Pontifícia Universidade Católica do Rio de Janeiro, PUC-Rio) is a Jesuit, Catholic, pontifical university in Rio de Janeiro, Brazil. It is the joint responsibility of the Catholic Ar ...
Valuing Real Options: Frequently Made Errors
Prof. Pablo Fernandez, IESE Business School
IESE Business School is the graduate business school of the University of Navarra. Founded in 1958 in Barcelona where its main campus is located,López, T. & Pampliega, J“La fundación del IESE (1956–1958)” Universidad de Navarra, Bibliotec ...
, University of Navarra
, image = UNAV.svg
, latin_name = Universitas Studiorum Navarrensis
, established = 17 October 1952
, type = Private, Roman Catholic
, chancellor = Fernando Ocáriz Braña
, president = María Iraburu Eliz ...
Identifying real options
Prof. Campbell R. Harvey. Duke University
Duke University is a private research university in Durham, North Carolina. Founded by Methodists and Quakers in the present-day city of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco and electric power industrialist James ...
, Fuqua School of Business
An introduction to real options
(Investment Analysts Society of Southern Africa
The Investment Analyst's Society of Southern Africa (IAS, IASSA) is the liaison body for the financial analyst profession in South Africa. It is based in Johannesburg South Africa, with members from Cape Town, Durban and throughout the region.
Mem ...
), Prof E. Gilbert, University of Cape Town
The University of Cape Town (UCT) ( af, Universiteit van Kaapstad, xh, Yunibesithi ya yaseKapa) is a public research university in Cape Town, South Africa. Established in 1829 as the South African College, it was granted full university statu ...
Decision Making Under Uncertainty—Real Options to the Rescue?
Prof. Luke Miller & Chan Park, Auburn University
Auburn University (AU or Auburn) is a public land-grant research university in Auburn, Alabama. With more than 24,600 undergraduate students and a total enrollment of more than 30,000 with 1,330 faculty members, Auburn is the second largest uni ...
Real Options Whitepapers and Case-studies
Dr. Jonathan Mun
Real Options – Introduction
Portfolion Group
How Do You Assess The Value of A Company's "Real Options"?
Prof. Alfred Rappaport Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
and Michael Mauboussin
Some Important Issues Involving Real Options: An Overview
Gordon Sick and Andrea Gamba (2005).
Real Power of Real Options, Leslie and Michaels (1997)
Keith Leslie and Max Michaels McKinsey Quarterly, 1997 (3) pages 4–22. Cited by Robert Merton in his Nobel Prize Acceptance Speech in 1997. McKinsey classic - Reprinted in McKinsey Anthology 2000 - On Strategy. Cited in McKinsey Anthology 2011 - Have You Tested Your Strategy Lately.
Journals
Journal of Real Options
Journal of Real Options and Strategy
Calculation resources
Prof. Aswath Damodaran, Stern School of Business
Prof. Steven T. Hackman, Georgia Institute of Technology
{{DEFAULTSORT:Real Options Analysis
Corporate finance
Options (finance)
Capital budgeting