Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Equation 1 illustrates how the travel-time reliability option can be formulated following standard
insurance options formulations, i.e., recasting an insurance option as a “speed guarantee insurance”
policy. From the mathematics of the underlying options theory, we know that (all other things
being equal) the options value of a speed guarantee (and, hence, the cost of unreliability of
speeds):
• Increases with the variability of speeds;
• Increases with the guaranteed speed;
• Decreases with the length of the contract; and
• Decreases with the average speed.
Absent any quantification of the options value, these insights are helpful in understanding how the
characteristics of unreliability, or the benefits of remediation of unreliability, are affected by
statistical properties of unreliability.
Two of the elements in the travel-time reliability option are the interest rate and the option length.
The value of the interest rate used in the formulation should be the real, annual riskless rate of
return. This rate varies somewhat with macroeconomic conditions, but should reflect the real
discount rate the market is applying to value funds received in the future versus today. This is also
called the "time value of money" in finance parlance. The interest rate in the implementation of
the Black-Scholes formula should be a low, single-digit annual rate in the vast majority of
macroeconomic settings. The option survives for a fix amount of time, calculated from the lowest
5% speed implicit in the speed distribution. This could be smaller or larger. It is done to avoid the
complexity of valuing serial options when multiple road segments, each with its different speed
distribution is involved. In this sense, it is akin to what is called a "capped" option, and imparts a
conservative value (lower) to the option value. This value (and hence the assumed life of the put
option (insurance contract) can be changed by the user.
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-10