Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Basically, the objective of these adjustments is to account for any overvaluation
caused by not meeting the “no arbitrage” condition. All three methods,
therefore, decrease the option value, making it more conservative.
Hence, development of real options and proper adjustment make development of a real option
possible, despite the fact that the commodity is not traded in a market where the arbitrage
condition is necessarily assured.
Damordaran (2005), The Promise and Peril of Real Options, provides a relatively accessible
treatise of the Black-Scholes formula and real options. In addition to providing an introduction to
the use of options, the paper includes discussion of the conditions for formulating real options and
a comparison of a real options approach to decision-making under uncertainty in contrast to the
more traditional discounted cash flow models.
A Real Option for Travel Time
To illustrate the applicability of options theory to the issue of travel time, let us examine the
phenomenon of unreliability, which occurs on a relatively frequent basis over the course of a year,
and how it might be analyzed using options theory. Imagine that a single link of a network is
involved, and that we have observed the speeds and resulting travel times on this link for many
days. Assume that those observations have led us to the conclusion that the travel time has an
average value, but considerable variation in value around that average. That is, travel times on any
specific day are unlikely to be the average, but rather something above or below the mean. (Put
differently, the link does not provide reliable service.) Further, our observations reveal that, over
the period of our observation, the travel times experienced are distributed log-normally.
We are interested in devising a succinct measure of the unreliability of this link. One way to do
that is to ask the question, "How much longer is the travel time I would accept in return for no
uncertainty about the travel time?" This question sounds very much like the questions that arise in
deciding how much one might be willing to pay to insure property. Since insurance contracts can
be represented by options, the question pertaining to travel-time unreliability can be answered with
the right formulation and parameterization of an options formula.
This travel time reliability option formulation is derived from options representations of insurance.
In other words, the basic insight of the approach is that one can think of unreliability as analogous
to the occurrence of an undesirable outcome in some random event context (e.g., an accident that
impairs the value of a car). In an auto insurance context, one can think of the insurance policy as a
mechanism for compensating the driver for any lost value due to an accident during the life of the
contract. Carrying this notion over to travel-time reliability, one can imagine that an insurance
policy could be crafted that compensated the driver for the unexpected occurrence of speeds below
the expected (average) speed. Such a policy does not exist for daily vehicle travel, although such
policies do exist for long trips (e.g. overseas travel insurance). So, if one accepts that the
CONCEPT of speed insurance makes sense, then the Black-Scholes formulation we are using
makes sense and one can calculate the speed-equivalent "premium" to be assured compensation for
encountering speeds less than the mean (expected) speed.
Thus, the premium of our insurance contract is the excess delay we are willing to pay to be
guaranteed a travel time equal to today's average. The specific mathematics of this are presented
later, but this example illustrates how travel-time uncertainty can be abstracted from to facilitate
valuing the unreliability of a road system. Specifically, the real option formulation allows us to
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-6