Real Options Selected Bibliography:
the Dixit & Pindyck Book

The "Selected Bibliography" list covers many important aspects of the options thinking. There are comments, for each book or paper, available by clicking their titles. This selection begins with the main reference, a born-classic text-book by Dixit & Pindyck: the first text-book exclusively about the real options approach to investments. This bibliographical item deserves a more detailed comments, in view of their importance to the theory.

Dixit, A.K. & R.S. Pindyck (1994): Investment under Uncertainty
Princeton University Press, Princeton, N.J., 1994
. Click here for Marco Dias' comments.

See also in the Contributions Page, An Instructor's Manual: for the Dixit & Pindyck's Investment under Uncertainty textbook by Luiz Eduardo Brandão (in Portuguese).
See also this link with the same material plus some spreadsheets.

See also in the Contributions Page, Matlab files to solve some problems from the Dixit & Pindyck's Investment under Uncertainty textbook by Luke J. Sparvero. NEW!

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Dixit, A.K. & R.S. Pindyck (1994): Investment under Uncertainty
The book brings an excellent theoretical and practical combination of the new approach, with their mathematics and economic foundations insights, complemented with industry typical investments decisions examples, embedded with representative industry's data.. In many times, when presenting equations, the book gives both, an intuitive/heuristic explanation and a more rigorous mathematical development.
In a rare case, a paper was written and published (outside of the books' review section) about this book (Hubbard, 1994).

The book comprises twelve chapters divided into five parts:

  1. The Part I is the introduction with two chapters.

  2. The second part of the book is the "Mathematical Background" with more two chapters:

  3. The third part of the book is the "firm's decision" with three important and more practical chapters:

  4. The fourth part of the book is the "Industry Equilibrium" with two chapters, and is more useful for economists:

  5. The Part V, Extensions and Applications, comprises the three last chapters.

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Hubbard, R.G. (1994):

Investment under Uncertainty: Keeping One’s Option Open
Journal of Economic Literature, vol.32, December 1994, pp.1816-1831

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Tobin's q:

This neoclassical investment model due to the Nobel Laureate J. Tobin, 1969 ("A General Equilibrium Approach to Monetary Theory", Journal of Money, Credit and Banking, 1, February 1969, pp.15-29), compares the capitalized value of the marginal investment to its purchase (replacement) cost.. The ratio is the Tobin's q. If q > 1, the firm should invest. The firm stops the investment process when their marginal investment is at such level that q = 1. If q < 1 the firm should not invest. The capitalized project value can be the observed directly if is marketable, but frequently it is computed as the expected present value of the net cash flows.

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Jorgenson's user cost of capital:

This neoclassical investment model due to the D. Jorgenson, 1963 ("Capital Theory and Investment Behavior", American Economic Review, 53, May 1963, pp.247-259), treats the capital investment as a purchase of a durable good. The user cost of capital is defined by the rental cost of the capital, and is determined using parameters like the purchase price, opportunity cost of funds, depreciation rates, and applicable taxes. The theory compares the value of an incremental unit of capital (marginal product) and the user cost (or rental cost): the firm invests when the marginal product is greater than the user cost and stops when an equality is reached.
In this model and in the Tobin's q model, the dynamics is considered (not satisfactorily) with adaptations such as "adjustment costs" and "delivery lags".

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Hysteresis in Economics:

The firm's status (if is active or if is idle) in the economy is path dependent, for a range of the firm's output price. This concept is important at firm level (entry & exit models) and also at macroeconomic level, in the studies of the aggregated investment from a specific sector of the economy, and sectorial policies.
When considering an investment and abandonment (entry & exit) together, the firm's optimal decision is characterized by two thresholds: one firm's output high price level, when the firm invests in production, and one low price level, when the firm abandon the project. Now suppose the current level of the price is somewhere between these two threshold: What's the status of the firm? Depend of the recent prices' fluctuations history. If the price descended from a high level that induced entry to many competitive firms, then the firm's status remain active. However, if the actual intermediate level was recently preceded by a low prices' level (that induced exit) then the firm remain idle. Or, as pointed out by the book, "the current state of the stochastic variable is not enough to determine the outcome in the economy; a longer history is needed. The economy is path dependent".

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Dynamic or Expanded NPV:

This expression has been employed by Trigeorgis in several papers, but the concept can be employed also to refer the NPV calculus in Dixit & Pindyck's Chapter 2.
As Trigeorgis points out,
Expanded (dynamic) NPV = static NPV + 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 project opportunities portfolio, the different "synergy effect" in each portfolio combination, can be added to the above expression, if relevant.

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The "bad news principle":

In a world with uncertainty , a "good" project (with positive net present value) can be postponed if a firm can wait to invest, because of the "bad news principle": there is a positive probability of a downward price movement, so that the waiting avoids the possibly losses from the project investment. The threshold price (that warrants immediate investment) depends of the size of the downward movement (not of the upward movement size) and the probability (besides the investment cost, of course), as shown in the equation 16, p.41.
This "bad news principle" was first pointed out by Bernanke, 1983 ("Irreversibility, Uncertainty, and Cyclical Investment", Quarterly Journal of Economics, 98, February 1983, pp.85-106), and some ideas can also be found in Cukierman, 1980 ("The Effects of Uncertainty on Investment under Risk Neutrality with Endogenous Information" ).
A nice and instructive argument is presented by Dixit, 1992 (Investment and Hysteresis, Journal of Economic Perspectives, vol.6, no 1, Winter 1992, pp.107-132, see p.123) illustrating the "bad news principle": Why the Japanese firms (despite its larger fixed costs) are more aggressive investors than the American ones? Because they are protected from the downside risk through the government supports. Then the value of waiting to invest is quite small, because the downside movement potential is small.
For disinvestment (abandon) the argument turns around and becomes the "good news principle": the option value of keeping the operation alive is governed mainly by the upside potential.
See also, in the tutorial page: "The two sides of the uncertainty"

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Bellman's Principle of Optimality:

"An optimal policy has the property that, whatever the initial action, the remaining choices constitute an optimal policy with respect to the subproblem starting at the state that results from the initial actions"
(Dixit & Pindyck, 1994, p.100)

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Function G(P) Method

This function is defined by the difference of value between the active firm and the idle one (original idea from Dixit, 1989). This function is only defined between the two thresholds (the thick part of the curve). This function helps the comparative statics job, too.
The geometric approach permits a graphical solution for the investment and abandonment thresholds (see footnote at p.220). In a very simple Excel sheet, I performed this method with success: with average of 4 iterations (3 minutes), I got the solution with error less than 0.1 %.

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Ex-ante Capacity Choice

In many projects (such as ships, factories, and upstream oil industry) we have an ex ante choice of scale, but prohibitively ex post adjustment in scale. In some situations the optimal is the largest capacity (if there is a increasing returns of scale for the largest scale region), even if is necessary wait for the output price reaches the threshold, and even if the other alternatives' threshold is under the market output price level. In others situations an intermediate scale may be the optimal choice (if there is decreasing returns of scale AND the elasticity of output with respect to investment is also decreasing). In others situations, the optimal is a binary decision between the smallest and the largest scale.
See an excellent exposition of this, with graphical and heuristic argument in the paper of Dixit (1993, Economic Letters, vol.41, pp.265-268).

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