Answer: Real options theory provides new insights on this very interesting and important application.

A large Petrobras-PUC research on this topic is finishing in 2004.

The aim of this research was the comparison of alternatives of oilfield development,
alternatives of investment in information, alternatives with option to
expand, etc., before commit a large investment in an offshore oilfield
development. The project topic covered in this FAQ finished in 2003, with a C++ software and a paper by **Dias & Rocha & Teixeira (2003)**, submitted to publication.

Let us analyze the case of mutually exclusive
alternatives to develop an oilfield. One simple model is presented by Dixit: "Choosing Among Alternative Discrete Investment Projects Under Uncertainty". *Economic Letters*, vol.41, 1993, pp.265-288.

This model is summarized below, with a little adaptation using the
concept of economic quality of a developed reserve(**q**).

If the oil price values P and one barrel of reserve values V, the quality
**q = V/P**. Here the normalized (by B) net present value **NPV/B = q P - D**,
where B is the reserve volume (number of barrels) and D is the normalized (by B) development cost (in present value).

OBS: In more recent papers I call V = q P B, but in this FAQ the notation is V = q P because we are working with normalized values ($/bbl) instead $.

The alternatives have different investment costs. Higher investment alternatives have benefit of faster production (more wells and/or higher processing facilities capacity) and/or lower operational costs. What is the optimal capital intensity under uncertainty?

First, let us see the best decision at the expiration. The picture below illustrates this case:

Higher quality q means higher inclination in the chart above.

Before the expiration the analysis is a bit more complex. One
alternative alone can be "deep-in-the-money", but the existence
of other alternatives can change this, and the manager can wait and
eventually to invest in a larger scale alternative.

The picture below shows this case.

The alternative 1 could justify an earlier investment if the inclination
(the reserve quality) become a bit more inclined.

Other important point is: with passage of time, the options curve move
down and for a region of prices, the option curve of alternative 2 can be
below the option curve of the alternative 1, so that is possible to choose
an earlier exercise of alternative 1 for prices at or above the P_{1}*
and lower than the intersection of the payoffs from alternatives 1 and 2.

It is easy to get the curves for the option alternatives with
spreadsheets like *Timing*. To compare, superpose the option curves and look for the higher one. With this practical approach we can see some special cases not addressed before by Dixit (1993). Even being an approximation (see below why), the numerical error on the value of the option is very small so that it possible to see that in most cases there is an ** intermediate waiting region** between the exercise of alternatives 2 and 3. So that for P > P*

Motived with this somelike surprising experimental early result, in 2000 were started two projects between PUC and Petrobras - from the Pravap-14 research projects portfolio, which confirmed this hypothesis. One Pravap-14 project was a more flexible and general determination of the optimal rules regions by using genetic algorithms (developed with Electrical Engineering Department). The other Pravap-14 project was more rigorous (but specific for simpler cases) using the traditional

By using a C++ PRAVAP-14 software developed at Industrial Engineering Department (PUC-Rio), it is possible to get the following thresholds chart showed below (and presented at MIT Seminar on Real Options, May 2002).

Working independently and with perpetual options, Décamps &
Mariotti & Villeneuve (2003) proved mathematically that the waiting
region around the point of indifference between NPV_{2} and NPV_{3}
* always* occurs (non-empty region) if sometimes is optimal
to invest in alternative 2. They showed that if "

Probably the conclusion from Décamps & Mariotti &
Villeneuve (2003) is even more general, being also true for finite-lived
options *except* at the expiration.

I thank to Professor Thomas Mariotti for letting me know about this paper
and for the nice discussion.

With this new insight in mind, we can *correct* the Dixit's option
value chart by setting a case that always occurs in the figure below
(analogous to Figure 1 from Décamps & Mariotti &
Villeneuve, 2003):

In the above figure, the option curve (red line) in the superior part of
this figure (between P_{W23} and P*_{3}) is the
intermediate waiting region. Décamps & Mariotti &
Villeneuve (2003) showed that this region always exists (if sometimes is
optimal exercise alternative 2, as occurs in the figure).

Numerically the error can be small if exercising the option (higher NPV as
suggested by Dixit in 1993) rather than waiting in this intermediate
optimal waiting region. So, even not being correct, the error using the
Dixit's insight can be small in practice. However, the size of the waiting
interval (between P_{W23} and P*_{3}) can be a large
range.

The full results from the Pravap-14 project (including cases with mean reversion) is reported in a paper by **Dias & Rocha & Teixeira (2003)**, submitted to publication.