Real Options Selected Bibliography: Other Books.

The following selection covers many important aspects of the options thinking and complements the lessons from the previously analyzed Dixit & Pindyck book. There are comments, for each book, available by clicking their titles (ALL COMMENTS AVAILABLE).


Brealey, R.A. & S.C. Myers (1991): Principles of Corporate Finance
Chapter 21, McGraw-Hill, Inc., fourth ed., 1991

Trigeorgis, L., (Ed.) (1995):
Real Options in Capital Investments: Models, Strategies, and Applications
Praeger Publisher, Westport, Conn., 1995

Lund, D. and B. Øksendal, (Eds.) (1991): Stochastic Models and Options Values,
New York: North-Holland, 1991

Shimko, D.C. (1992): Finance in Continuous Time. A Primer
Kolb Publishing Company, 1992

Copeland, T. & T. Koller & J. Murrin (1990):
Valuation - Measuring and Managing the Value of Companies
Chapter 12, John Wiley & Sons (Ed.), 1990

Lopes, E.P. (2001):
Opções Reais - A Nova Análise de Investimentos ("Real Options - The New Investment Analysis"), in Portuguese.
Ed. Sílabo, Lisboa, 2nd edition, 2001

Forthcoming the analysis of more two books:
Trigeorgis, L., (1996):
Real Options - Managerial Flexibility and Strategy in Resource Allocation
The MIT Press, 1996

Dixit, A.K., (1993):
The Art of Smooth Pasting
Harwood Academic Publishers, 1993

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Brealey, R.A. & S.C. Myers (1991): Principles of Corporate Finance - Chapter 21
A classic corporate finance book, dedicates three chapter for options, one of then about real options. An interesting example of growth options (or option to make follow-on investments) with the computer "Mark I". There are others examples and an overview, at an introductory level, of the Real Options Approach.
One of the authors (Myers) coined the term "Real Options", in 70's (see Myers, S.C.: "Determinants of Corporate Borrowing", in Journal of Financial Economics, no. 5, November 1977, pp.147-175.
The authors point out that discount cash flow (DCF) does not reflect the value of management: "DCF implicitly assumes that firms hold real assets passively. It ignores the options found in real assets". When uncertainty is present, value calculations "is not a simple matter of discounting",
The abandonment option is presented into put option analogy framework, with two and three periods examples, followed by the general binomial approach.
The timing option is presented, and so the distinction between a project with timing flexibility and "now or never" project. An example with three periods is analyzed.
The link between options approach (using binomial method) and decision tree analysis (DTA) is also presented. The authors (p.525) teach: "there is no single, constant discount rate for options because the risk of the option changes as time and the price of the underlying asset change. There is no single discount rate inside a decision tree".
The "checklist" section shows the various types of financial options (American, European, calls, puts, with and without dividends) and the application to real investments, with focus on early exercise role for real investments.
This is one of best introductory texts on real options.
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Trigeorgis, L., (Ed.) (1995): Real Options in Capital Investments: Models, Strategies, and Applications
Other book exclusively about real options. Although this is not a text book (is a collection of papers), the papers are grouped into five thematic parts, preceded by the editor (Trigeorgis) very interesting paper, which he presents an overview of options literature: see for example the excellent table 1.1, which is presented the various options types, and for each type of option, are showed a short description, the applications, and the main bibliography related. The author learns that many real options occur naturally (exogenous to the firm) and others may be planned and built in at some extra cost (many flexibilities of future expansion, and input or output switching options). He also presents the expanded (strategic) NPV equation.
The Part I, "Real Options and Alternative Valuation Paradigms" comprises three papers, one comparing the real options approach with two others modern and interesting methods (dynamic DCF analysis and decision analysis); the second one focus the decision analysis (preference-dependent approach), presenting the concept of market utility; and the last one presents the linkage of capital budgeting and strategic planning.
The Part II, "General Exchange or Switching Option Interdependence", comprises also three papers, the first one about the value of flexibility as a framework for a general model of real options; the second one about the valuation of American Exchange Options, which the author (Carr) develop a general formula for pricing these options (with important special cases); and the last one illustrate the interactions between many different options types, using both Geometric Brownian and Mean Reverting motions, concluding that the incremental contribution to project value of each type of option can be attenuated by substitute options (timing to invest and abandonment) and enhanced by complementary options (temporary stopping and growth options). The part III, "Strategy, Infrastructure, and Foreign Investment Options", comprises again three papers, the first one showing the role of real options in mergers, acquisitions and divestitures; the second one describing the real options in Japan, where some real options are unique to the Japanese system or at least more widely seen among Japanese firms; and the last one analyzing entry & exit of multinational firms, which the effect of the volatile exchange rates depends on whether the project is of fixed scale or of variable scale.
The Part IV, "Mean Reversion/Alternative formulations in Natural Resources, Shipping, and Start-up Ventures", comprises three papers, one showing the effects of mean-reverting process on projects with different length, using a model of exponential decay in the term structure of the volatility; the second one focusing shipping applications using a more simplified mean-reverting process (arithmetic Ornstein-Uhlenbeck); and the last one analyzing the start-up venture projects, using an alternative jump formulation for growth option valuation.
The Part V, "Other Applications: Pollution Compliance, Land Development, Flexible Manufacturing, and Financial Default", comprises four papers, the first one is about the options faced by a firm (Georgia Power) due the environmental requirements (Clean Air Act), such as buy or sell pollution allowances, investment in expensive scrubbers, and switch to the more expensive low-sulfur coal; the second one is a application of timing options for land development, which the assumption of portfolio perfectly correlated with the project is relaxed (correlation less than 1, but constant), among others features; the third one is a valuation application for multiproduct projects, which considers both the output yield and the input prices as stochastic in a lattice contingent claims framework; and the last one is an application for risky debt valuation, modeled as a put option, extending previous models of corporate liabilities, by incorporating features of the bankruptcy law to value default risk.
All the papers' authors are eminent Ph.D. or DBA, and this book can be used as cases book in MBA schools or as reference for researchers.
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Lund, D. and B. Øksendal, (Eds.) (1991): Stochastic Models and Options Values,
This book is a collection of papers, edited by Norwegian professors from Economics and Mathematics Departments of the University of Oslo, and is organized into four parts. This book is a more advance treatment (interesting for M.Sc and Ph.D. students, not for MBA courses) in comparison with the others books listed in this page.
The Part I, "Introduction", comprises two papers, the first one is an overview of real options theory, with considerations about the growth rate, rate of return shortfall/convenience yield, and risk adjusted discount rate, and comments about some aspects from the papers of the same book; the second paper is a summary (by mathematical view) of stochastic control theory, with emphasis in dynamic programming, introducing some theorems (like the theorem 5, about the existence of an optimal control, valid for many problems), and about singular control, for problems which the usual smooth control (and the Bellman equation) not hold.
The Part II, "Financial Option Theory Applied to Real Investment", in a more practical way, comprises 5 papers. The first one, compares four models to convenience yield, three of then as function of the spot price (linear, quadratic, and maximum between a constant value and a linear in the spot price), and the last, named "autonomous model", which the term structure of the convenience yield is modeled by a mean-reverting stochastic process, and empirical analysis is performed for many commodities (including heating oil). The second paper, again about convenience yield, is specific for the crude oil, again shows empirical evidence to model the term structure of the convenience yield as a mean reverting process, and presents an application to value long-term oil-linked bonds. The third one, deals with an oil field development in Norway, which the Government wishes to be initiated not later than a fixed date (a constraint imposed due the unemployment), analyzing the possibility of the Government buy back the oil field undeveloped and can undertake immediate development, or can fix a future date which the national oil company must starts the development. The lost value due the reduction in the managerial freedom degree (named "cost of a promise" by the author) is computed for these cases comparing with the unconstrained case (perpetual opportunity) which reaches, at the traditional break-even price, 250 millions US$ (the DCF method doesn't see lost value at this price). The fourth paper is an econometric work about the predictions of the investment aggregate, showing that neoclassical models (like marginal Tobin's q, see also the comments for Dixit & Pindyck book) fails, even using sophisticated models incorporating delivery lags, and also the difficulty of econometric modelling irreversible investment under uncertainty (equations "extremely" nonlinear and difficulty to measure key parameters of risk), although the author shows qualitative evidences (uncertainty delays investment) and points some ways to perform quantitative empirical tests, to find how large the uncertainty matters on aggregate investment. The last paper is an interesting historical overview of the concept of "options", presenting three different traditions: (a) the financial tradition, with emphasis in assets' value calculation; (b) economic tradition with emphasis in decision's rule (to make a choice), like early works by Arrow & Fisher (1974) and Henry (1974) (1), named AFH model, and has the same sense as financial tradition (with different emphasis); and (c) the Schmalensee (1972), Bohm (1975) and Graham (1981), also with economic choice emphasis (2), but relies on consumers being risk averse, and can be negative. The author points the similarities between the financial and the AFH traditions, with an example of hybrid method about the uncertainty in consumer surplus, suggesting new applications of the financial tradition to problems that has been dealt in the AFH framework, such as the consumer surplus.
The Part III, "Stochastic Control and Dynamic Programming", comprises four papers, three of then with mathematical emphasis. The first one, is an economic paper about sequential investment (in contrast to lumpy investment), where the firm incrementally expands capacity in response to stochastic demand variations, which is solved using the advanced tools like singular stochastic control mentioned in the first part (see p.28), and the author says that the Pindyck model (1988) is a special case of his model, but this is not clear (see comments at p.14). The second one is about the high contact condition (also known as smooth pasting condition) as a sufficient optimization condition for problems of optimal stopping, and the author examines the multidimensional case for a general class of finance/economic problems (including Brennan & Schwartz, 1985 model, as an example), extending results of early papers. The third paper considers the invariant control, which the production is uncertainty (besides the price uncertainty) as is the case of a firm with several mines, where the rewards from each mine are determined by the specific metal content of the ore and the metal price (uncorrelated process), and for others problems which the stochastic process are not independents. This paper identifies situations in which this correlation doesn't influence the optimal policies (including an application of an optimal policy for switching extraction between two oil fields), and the solution for uncorrelated process is valid also for correlated process. The last paper examines the shadow price role in decision making under uncertainty, presenting a generic optimization problem, and two kinds of constrains (resource and information, the latter incorporates a process of learning), in a discrete time approach, using Lagrange multipliers.
The Part IV, "Statistical Models of Natural Resource Exploitation", comprises two papers. The first one is an application for fishing industry (mainly for a regulatory agency), which the stock of fish is an unobserved stochastic variable, and examines how to extract information optimally. The second and last paper, is a sequential decision problem (continue the production or abandon an oil field) which examines only the technical uncertainty effect, which the optimal decisions is made considering the reduction of the technical uncertainty variance, due the informations collected by the production (see additional comments), and the authors presents numerical examples, one of then demonstrating the value of a flexible production technology.

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Shimko, D.C. (1992): Finance in Continuous Time. A Primer
This thin book explain modern finance methods in a concise way, and is useful for both financial and real investment applications. The book is divided into four chapters, with lots of exercises at the ending of each chapter. In contrast with most other texts, this one frequently uses Laplace transformations to solve the differential equations (used also in Cox & Miller, 1965, a book about stochastic processes).
The first chapter is an overview of stochastic processes (arithmetic and geometric Brownian, mean-reversion, jump process), stochastic tools (Itô Lemma), and correlations between two stochastic process (see the table at p.16, for a summary of multiplication for differential variables).
In the second chapter, the frequently occurring differential equations is presented, which has the same general format in finance problems, and also important questions such as the homogeneity of these equations, the discount rate for the assets (showing that the solution is of the same form in risk-averse and risk-neutral economies), and an introduction of recursive techniques in asset valuation is also presented.
The third chapter explain the arbitrage principle with applications for asset valuation. European and American options are analyzed, and the smooth pasting (or high contact) optimal condition is presented for the American one.
The last chapter deals with optimal as a maximization of present values, first with the time-homogeneous problem (a infinitely lived asset or project), followed by extensions: the multiple state variables case, and the time non-homogeneous case. Closing the book some aspects of the classic Merton (1971) optimization problem for consumption and portfolio rules, is presented.

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Copeland, T. & T. Koller & J. Murrin (1990):
Valuation - Measuring and Managing the Value of Companies
In this book about valuation of companies, the authors (from a consultant firm) dedicate one chapter for real options ("Using Option Pricing Methods to Value Flexibility"). This chapter points that "For valuations, it is important to remember that options can be found on both the assets and the liabilities sides of the balance sheet".
Using many simple examples, with event and decision trees analysis (DTA), is showed that NPV analysis often undervalues assets because it fails to account for the managerial flexibility (options) embedded in business decisions. The authors illustrate that "option pricing is a generic form of decision making that encompasses NPV and DTA as special cases".
There is a little example of oil extraction (pp.359-360) where the option adds 21% to "OILCO" value. Others examples: mining (option to shut-down/reopen and abandon, increases in more than 60% the mine value); Pharmaceutical R&D (option adds more than 80% of the project value); and so on. On the other side of the balance sheet, for the liability options, others examples are included.
In short, it is a good introductory explanation for real options, with focus on valuation of companies.
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Lopes, E.P. (2001)
Opções Reais - A Nova Análise de Investimentos ("Real Options - The New Investment Analysis"), in Portuguese

The author, Professor Eurico Pereira Lopes, from both Universidade Técnica de Lisboa and Universidade Lusíada de Lisboa, send me the following short description of his book:

This book addresses Contingent-Claims Analysis in the valuation of investment projects, including within the financial analysis, those components of value linked to the operational and strategic flexibility, which, due to the failure of traditional DCF capture techniques, are left to intuition and experience of managers.
It identifies, through Case Study a new type of real option which I designate "partial guaranteed placed production option," thus contributing to the extension of Taxonomy of Real Option, and in turn, to the continued emergence of a Theory of Real Options. It proposes as criterion of choice of investments opportunities in real assets the Strategic Adjusted Net Present Value: Strategic Adj. NPV = Adj. NPV + Value of Options from Active Management. You can consult to obtain a complete information about the book in Portuguese.

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Expanded or Strategic NPV:

This expression has been employed by Trigeorgis in several papers.
As Trigeorgis points out,
Expanded (strategic) NPV = static (passive) NPV + value of options from active management (Option Premium)
The "Option Premium" can be from the (most) relevant option, or a "Combined Option Value" (in a multi-options interactions context). In large companies, with a large portfolio of project opportunities, the different "synergy effect" in each portfolio combination, can be added to the above expression, if relevant.

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Note (1):

The Arrow & Fisher and Henry early papers, can be seemed as the qualitative foundations of modern irreversibility and real options (flexibility) concepts, although only after the finance options theory developments, the modern quantitative approach for real options was established.

Note (2):

The option concept in this context is a kind of risk premium for risk averse consumers, because uncertainty over future valuations of an environmental amenity (see Dixit & Pindyck, 1994, footnote p.426), and is very different of the option concept adopted in this site for economic decisions.

Sufficient Optimization Condition (high contact or smooth pasting)

This sufficient optimal condition was first introduced by Samuelson's paper (1965), with both heuristic argument and a rigorous proof in a mathematical McKean's appendix for this paper. Samuelson also introduced the stochastic calculus in finance applications.

Optimal Stopping

Optimal stopping problems means a binary decision (for ex.: wait or invest), and defines two regions named, respectively, continuation region (waiting) and stopping region (investment). The line that separates the two regions is named free boundary and defines the optimal points for economic decisions (or threshold prices line) like investment and abandonment. See for example, Dixit & Pindyck (1994, pp.103, 108-109, and 128).

Invariant Control

Invariant control means an optimal strategy that remains optimal even if the instantaneous stochastic payoff is multiplied by another (either independent or correlated) stochastic process. See Lund in the same book (p.15).

Note for Shadow Prices and Lagrange Multipliers

For the shadow prices that results from a learning by investing process, see in "Tutorial", the "Technical Uncertainty" item.
For a continuous time application of Lagrange multipliers, see the very interesting paper of G. Chow (1993).

Additional Comments:

The authors suggest, for investment decisions, that should be considered the abandon decision with the technical uncertainty and learning effects. However, as showed by Bjerksund & Ekern (1990), if you have considered the timing option, the additional abandon option has little effect in field value.
Other comment is that the several reservoir informations after the production starting, has little effect for additional variance reductions (in general, the reduction is significant at the initial stages, with decreasing marginal contribution to variance reduction).
The Stensland & Tjøstheim paper is correct and important to set the key role of technical uncertainty: the variance reduction with time by doing (producing or investing), not by waiting (see Dixit & Pindyck, 1994, chapter 10, section 4), but I believe that a far more interesting application in petroleum is for exploration investments decisions, in large oil companies, after the rights to explore a tract to be acquired (see also Dixit & Pindyck, 1994, footnote 3, p.397). The qualitative conclusions in the example of platform choice (mobile platform or fixed platform) are correct, and explains the large use of floating production system in many situations (mainly in Brazil and North Sea) even when the flexible system is more expensive or has a slight lower operational efficiency. The flexible technology is more valuable when technical uncertainty is relevant than when the economic uncertainty is predominant, at least for petroleum E&P applications, because the alternative use for the mobile platform is in the same petroleum E&P industry.

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