Stochastic Programming - Index of

6 STOCHASTIC PROGRAMMING
We observed from Table 1 that the expected Net Present Value (NPV)
of Decision 4, i.e. the decision to develop Lot 2 and build a plant, equals
30. Standard theory tells us to invest if a project has a positive NPV, since
that means the project is profitable. And, indeed, Decision 4 represents an
investment which is profitable in terms of expected profits. But as we have
observed, Decision 3 is better, and it is not possible to make both decisions;
they exclude each other. The expected NPV for Decision 3 is 195. The
difference of 165 is the value of an option, namely the option not to build
the plant. Or to put it in a different wording: If your only possibilities were to
develop Lot 2 and build the plant at the same time, or do nothing, and you
were asked how much you were willing to pay in order to be allowed to delay
the building of the plant (at the 10% penalty) the answer is at most 165.
Another possible setting is to assume that the right to develop Lot 2 and
build the plant is for sale. This right can be seen as an option. This option is
worth 195 in the setting where delayed construction of the plant is allowed.
(If delays were not allowed, the right to develop and build would be worth 30,
but that is not an option.)
So what is it that gives an option a value Its value stems from the right
to do something in the future under certain circumstances, but to drop it in
others if you so wish. And, even more importantly, to evaluate an option you
must model explicitly the future decisions. This is true in our simple model,
but it is equally true in any complex option model. It is not enough to describe
a stochastic future, this stochastic future must contain decisions.
So what are the important aspect of randomness We may conclude that
there are at least three (all related of course).
1. Randomness is needed to obtain a correct evaluation of the future income
and costs, i.e. to evaluate the objective.
2. Flexibility only has value (and meaning) in a setting of randomness.
3. Only by explicitly evaluating future decisions can decisions containing
flexibility (options) be correctly valued.