Lecture Notes in Management Science (2012) Vol. 4: 169–178
4th International Conference on Applied Operational Research, Proceedings
© Tadbir Operational Research Group Ltd. All rights reserved. www.tadbir.ca
ISSN 2008-0050 (Print), ISSN 1927-0097 (Online)
Differences between financial
options and real options
Tero Haahtela
Aalto University, BIT Research Centre, Helsinki, Finland
tero.haahtela@aalto.fi
Abstract. Real option valuation is often presented to be analogous with financial options
valuation. The majority of research on real options, especially classic papers, are closely
connected to financial option valuation. They share most of the same assumption about
contingent claims analysis and apply close form solutions for partial difference equations.
However, many real-world investments have several qualities that make use of the classical
approach difficult. This paper presents many of the differences that exist between the financial
and real options. Whereas some of the differences are theoretical and academic by nature,
some are significant from a practical perspective. As a result of these differences, the present
paper suggests that numerical methods and models based on calculus and simulation may
be more intuitive and robust methods with looser assumptions for practical valuation. New
methods and approaches are still required if the real option valuation is to gain popularity
outside academia among practitioners and decision makers.
Keywords: real options; financial options; investment under uncertainty, valuation
Introduction
Differences between real and financial options
Real option valuation is often presented to be significantly analogous with financial
options valuation. The analogy is often presented in a table format that links the
Black and Scholes (1973) option valuation parameters to the real option valuation
parameters. Table 1 illustrates this analogy. All too often, however, the differences
between the two approaches are not discussed thoroughly. Furthermore, some of
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Lecture Notes in Management Science Vol. 4: ICAOR 2012, Proceedings
these arguments are rather academic by nature and do not reflect the practical concerns
of real option valuation. Discussion about the interpretation of the calculated result
and its theoretical correctness may be irrelevant, because the underlying assumptions
often contradict the reality quite harshly.
Table 1. Analogy between financial and real options.
Financial option
S
X
T

R
D
Real option
Value of the underlying asset, i.e. Present value of project’s or investment’s
stock price
cash flows
Amount of money to be invested or
Exercise (strike) price
received in launching (exercising)
the action (option)
Time until the option expires
Time until the decision must be made
Standard deviation (volatility) of Uncertainty about the future value
the value of the underlying asset (probability distribution)
Risk-free rate of interest
Risk-free discount rate
Dividends paid out by
Dividend like cash outflows or inflows of
the underlying asset
project over its life-cycle
Many real option valuation procedures derived from the financial option valuation
have the problem that they do not necessarily follow the same assumptions. For
example, financial option values may never be negative, whereas some real options
may have negative underlying asset values. If the valuation method does not take
this into account, it may provide strange and misleading results. Another significant
difference is that information on financial option valuation parameters is often
easily available for everyone in the markets. This does not hold for real options,
and this ambiguity should be considered both in the practical valuation and in
interpreting the calculated results. Also, the length of the investment periods is
typically different; as a result, uncertainty changes (usually reduces) more during
the real option investment. Table 2 is not a comprehensive listing of the differences
but instead shows certain elementary issues with several example references for
each topic.
Table 2. Differences between the financial and real options.
Financial option
Short maturity (usually
months)
Real option
References
Longer maturity with several Mun (2002); Triantis
years
(2005); Brach (2003)
Time-varying, usually
Brach (2003); Majd &
Volatility sufficiently stable
diminishing, volatility
Pindyck (1987)
Rather mean reverting in the Laughton & Jacoby
Follows better gBm
long run
(1993)
T Haahtela
Financial option
Real option
Underlying variables are
Underlying variable is equity free cash flows driven by
or asset price
competition, demand and
management
Not necessarily traded and
Marketable and traded
proprietary in nature, with
comparables information
no market comparables
Managerial decisions and
No possibility to control and
flexibility increase option
manipulate option value
value
Actively acquired by
Side bets
management
171
References
Mun (2002); Kyläheiko
et al. (2002)
Brach (2003); Copeland
& Antikarov (2005)
Copeland &Antikarov
(2001)
Copeland & Antikarov
(2001)
Mun (2002); Copeland
Management assumptions & Antikarov (2005);
Management assumption
and actions drive the value Kodukula & Papudesu
have no effect on valuation
of the real option
(2006); Kyläheiko et al.
(2002)
Competition and market
Competition and market
Trigeorgis (1996);
value drive value of the
value do not affect valuation
Trigeorgis (1988)
strategic option
Usually small (proportional)
Large scale decisions
Mun (2002)
values
Numerical accuracy more
Framing the option case
Amram & Kulatilaka
important
more important
(1999 );
Often rainbow and comTrigeorgis (1996);
Often single options
pound options (parallel and Copeland & Antikarov
sequential) with interactions (2005); Brosch (2008)
Closed-form solutions
Solved usually using closedand binomial lattices with
form PDE’s and simulation /
Mun (2002); Copeland
simulation of the underlying
variance reduction tech& Antikarov (2005)
variables (not on the option
niques
analysis)
Have existed for more than Practical use for
Mun (2002)
30 years
approximately two decade
Dependent on both
risk-free interest rate and
Dixit & Pindyck
Depends only on risk-free
risk-adjusted premium or (1994); Kulatilaka
interest rate
equilibrium rate in dynamic (1995); Teisberg (1995)
programming context
Different and sometimes
Ordinary payoff functions
Zhou (2010)
complex payoff functions
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Lecture Notes in Management Science Vol. 4: ICAOR 2012, Proceedings
Financial option
Real option
References
Volatility increase after
Huchzermeier & Loch
committed investments may
(2001); Brosch (2008)
have negative effect
Expected value may be
Option value known at
known, but it may still have Brach (2003)
exercise
fluctuations in the future
Majd & Pindyck
Timing of option payoff
(1987); Perlitz, Peske &
Timing of option payoff
delayed, not precisely
Schrank (1999);
known (immediate)
known, and may spread
Kodukula & Papudesu
over a period of time
(2006)
Exercise time or time period Exercise time, especially
Brach (2003); Copeland
(for American option) known optimal one, not necessarily & Tufano (2004); Triin the beginning
known
antis (2005)
May not have price for
Trigeorgis (1996);
Option has certain price to
acquiring the option or the Kodukula & Papudesu
acquire
price is unknown
(2006)
Can be leveraged
Cannot often be leveraged (Brach 2003)
(Brach 2003); Pindyck
Strike price may also be
Strike price often known
(1993); Kodukula &
stochastic
Papudesu (2006)
Triantis (2005);
Shared and proprietary
Proprietary possibilities
Trigeorgis (1996);
nature
Trigeorgis (1988)
Managerial skills and
Managerial skills and
incentives do not prevent
incentives may prevent
Triantis (2005)
value maximization
value maximization
May have information
Usually no information
Brach (2003); Copeland
asymmetries with arbitrage
asymmetries
& Antikarov (2005)
possibilities
May have fuzziness or amPrecise parameterization
Brach (2003)
biguity in parameter values
Owned, created and exer- Triantis (2005);
cised by the cooperative
Trigeorgis (1996);
Owned by one party
activity of more than one Smit & Trigeorgis
company
(2004)
Copeland & Antikarov
May not have negative
Underlying asset may have
(2005); Camara
values
negative values
(2002); Haahtela (2006)
Discrete information flow
Lint & Pennings
Continuous information flow with occasional managerial
(2000); Willner (1995)
reactions
Volatility increases always
beneficial
T Haahtela
Financial option
Real option
Mostly European by nature
Mostly American by nature
Computational efficiency
important
Can be diversified
Computational efficiency
less important
Cannot be diversified
Valuation parameters are
Valuation parameters mostly often secondary, derived
primary and observable
and estimated from the
variables
primary parameters of the
cash flow simulation
Sensitivity analysis based on More complex sensitivity
the ‘Greeks’
analysis
All options are known in the Some options may be
beginning
acquired during the project
Not necessarily ability to
Can be hedged
hedge
173
References
Copeland & Antikarov
(2005)
Amram & Kulatilaka
(1999)
Brandao et al. (2005)
Haahtela (2011b)
Haahtela (2010b,
2011b)
Brach (2003)
Copeland & Antikarov
(2001)
Another common problem is that many practitioners view the existing real option
valuation models as too complicated to use and even more so to explain (Triantis,
2005). These real options models are like “extreme sports” that looks impressive
but are hardly something that could be applied in a real business setting.
Another problem, once again more academic, is that the real options are investigated
according to the financial options lens far too often. Some purists may argue that
real option valuation should not be used unless it can be justified with a replicating
portfolio or a risk-neutral valuation approach. In practice, both of these approaches
require that the underlying asset and its information be available in the financial
markets. These arguments hold for financial options, but Stewart Myers (1977) who
originally suggested using options logic for valuing real investments, did not present
this requirement. Late, he also emphasized (e.g. in Cirano newsletter, 2004) the strategic
thinking behind the real option valuation and compared real options valuation as an
alternative for the net present value calculation. Luenberger (1997) in his book
Investment Science, also challenges the strict requirement for market-based data
and considers real options instead as a way to apply a backward rolling valuation
approach. Armstrong and Bailey (2005), rather than speaking of options, suggested
that several possibilities could be referred to as (operational) alternatives.
Borison (2005) and comments on his work of different real option valuation
approaches explain the distinction between different ‘schools’ of real option valuation.
Some authors tend to believe that the same strict assumptions that hold for financial
options valuation are required, whereas others believe that the same arguments of
comparable investments used to justify the net present value calculation are sufficient
for real options valuation. Woolley and Cannizzo (2005) stated that real options
should be shown and treated as a complement to rather than a replacement for
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Lecture Notes in Management Science Vol. 4: ICAOR 2012, Proceedings
discounted cash flow (DCF) by showing how real options are consistent with and
extends the power of DCF.
Another significant difference is related to the precision of the real option
valuation. Real option valuation, however, is no more precise or imprecise than
the quality of its input parameters. The so-called ‘garbage-in, garbage-out’ sentiment
also holds for real options, similar to other valuation methods. A high-quality real
option analysis with thorough sensitivity analysis is capable of revealing to the
decision maker how reliable the calculated results are. Also, as stated by Amram
(2005), valuing patents and early-stage technologies is intrinsically difficult, because
the degree and types of uncertainty that attend such projects effectively rule out
the possibility of precise valuation results. New thinking and models are needed,
and over time, a natural cycle of the model and data refinement emerges.
Several authors have recognized the need for new approaches in real option
valuation. Triantis (2005) stated that one must be careful about specifying
distributions for the underlying assets in a model, whether it is a specific
commodity price or demand or a bundled uncertainty in the form of the underlying
project value. In real options, distributions of the underlying asset differ often
significantly from the geometric Brownian motion assumed in Black-Scholes and
other related models. Models based on new distribution specifications will continue to
make valuable contributions to the academic literature and practice, as will research
that provides better guidance on how to estimate the nature of the distribution and
the key parameters involved. Another significant difference is the complexity of
the real options compared to the financial options. Real investments may have
several interacting real options, whereas financial options usually have straightforward
payoff functions.
Real option valuation approaches for tomorrow
Financial options can be valued using closed-form solutions and many tailored
one-of-a-kind –valuation procedures for different option types. Unfortunately, this
does not hold for real options. Whereas analytical closed-form models may provide
generalized scientific knowledge and managerial insights, they are not necessarily
of practical use in appraising investments. As Charnes (2007) noted, many purists
prefer to use only models that avail themselves of an analytic solution. When
confronted with a realistic complication that precludes an analytic solution, the
complication is simply assumed away. Practitioners, in contrast, wish to include
realistic complications and are happy to accept the trade-off of obtaining an
approximate solution using a simulation.
One alternative is to use simulation-based methods. Techniques that were
previously considered to be computationally expensive and not feasible are today
often the method of choice (Jäckel, 2002). Rather than using simulation directly
for path sampling (as Boyle, 1977, originally suggested) or numerical integration,
Monte Carlo simulation can be used to consolidate cash flow calculation uncertainties.
Most well-known of these approaches are the valuation framework of Copeland
T Haahtela
175
and Antikarov (2001) with the consolidated logarithmic volatility estimation and
the pay-off approach of Datar and Matthews (2004; 2007).
Lattice and tree-based methods are another suggested alternative. They are
accurate, robust, and intuitively appealing tools to value financial and real options
(Hahn, 2005). Lattices are also explained to and accepted easily by management,
because the methodology is straightforward to understand. This is valuable particularly
with sequential and parallel compound options, which is often the case in real
applications (Trigeorgis, 1996; Copeland and Antikarov, 2001). They can also be
applied to stochastic processes other than gBm, including mean-reverting, jumpdiffusion, and displaced diffusion processes. The present alternatives are much
more flexible and usable for real option practitioners than the original binomial
tree methods used for valuing financial options (e.g., Cox, Ross, & Rubinstein, 1979).
One example of an enhanced lattice method for real option valuation is
Haahtela’s (2010a) recombining trinomial lattice with changing volatility. It is
based on a displaced diffusion process that allows negative underlying asset values
and has a much wider spectrum of possible distribution forms than a commonly
assumed lognormal gBm process (Haahtela, 2006). The volatility (or displaced
volatility) is both time- and state dependent, which is essential for practical real
option valuation. The parameterization of the process is based on a simulated cash
flow; furthermore, it is straightforward and intuitive with a regression sum of
squares error method (Haahtela, 2011). This cash flow calculation may also include
embedded options whose values are based on choosing the optimal decision in
each time step during a single simulation run (Haahtela, 2010c). The trinomial tree
remains recombining and stable even with the changing volatility. Also, the forwardlooking cash flow estimators of the approach can be applied to sensitivity analysis
(Haahtela, 2010b; 2011b). Thus, decision makers can investigate how a project
value with several interacting options may change as a result of changes in uncertain
cash flow calculation parameters. The method also allows the decision maker to
inspect whether the uncertainty is in the form of ambiguity or volatility (Haahtela,
2008; Haahtela, 2012).
Another novel approach for real option valuation is to use the fuzzy pay-off
method (Collan et al., 2009). Fuzzy logic (Zadeh, 1965) was originally used for
financial option and real option valuation by applying it to the Black -Scholes
environment (see e.g., Carlsson and Fuller, 2000; Zmeskal, 2001; Yoshida, 2003;
Collan, 2004). As the name suggests, however, the fuzzy payoff method approach
combines the use of fuzzy logic with the idea of the payoff method (see e.g.,
Boyle, 1977; Angelis, 2000, 2002; Datar and Matthews, 2004, 2007). The approach
uses fuzzy numbers to represent the future distribution of expected option value
and applies fuzzy mathematics to calculate the option value. The future will
determine whether this stream of real option research and its applications will become
more widely applied than the other aforementioned approaches.
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Conclusions
As a result of the topics mentioned and listed in the previous two chapters, real option
researchers should focus on new streams of research that find practical valuation
approaches that are managerially more appealing, robust and intuitive. At the same
time, they should retain most of the good qualities of the more accurate option
valuation approaches. In practice this means that numerical methods and calculus
should be used rather than difficult mathematics. Simulation and lattice methods
are examples of such robust methods that allow simultaneously taking into account
many of the differences presented in Table 2. Closed form solutions are available
that can take into account one or two of the aspects mentioned in Table 2, but not
the majority.
In the end, the real value of any method is based on its practical relevance and
ability to help practitioners make correct and timely investments, or at least avoid
making clearly incorrect decisions. Academic real option research, rather than
holding too strictly to the theoretical correctness of the models, should focus more
on finding innovative and robust ways to value flexibility and investment under
uncertainty. These methods may be based on simulation, using fuzzy logic, system
dynamic models, new ways to apply decision trees, or even to some completely
novel approaches.
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