Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Step 2 – Calculate Certainty-Equivalent Value of Reliability
A. For this example, the European Put option is employed for the following
reasons:
• The European Put option gives us the traveler’s value of
unreliability for each trip made, given the observed or expected
speed variability. The value of unreliability can be multiplied by
the number of commuters and work days to tell us the commuter
value of unreliability for a period of time, appropriate for the
evaluation of a strategy.
• The European Put option is based on values of variables that are
distributed log-normally, as is the speed data on a facility leading
to a fitting application.
B. A value of 5.00% risk-free interest rate is chosen.
Thus, r = 0.05
C. The contract length (T-t), is calculated as the travel time to cover the segment
under consideration at the lowest 1% speed, determined using the mean logspeed
and the standard deviation of the log-speed. For this example the lowest
1% speed is 13.22 mph and the segment is 10 mile long. The contract length is
expressed in years since the interest rate is an annual rate.
⎛ 60 /13.22 ⎞
T − t = ⎜
⎟×
10 = 0.0000863 years
⎝365× 24×
60 ⎠
D. The certainty-equivalent value of reliability, PV (
T
,) t is calculated by first
calculating σ , d1 and d2. σ is calculated using the formula for volatility in
finance, which is the standard deviation of the log speed divided by the square
root of the contract length:
α 0.3635
σ = = = 39.12
( T − t) 0.0000863
2
ln( VT
/ I) + ( r+ σ / 2)( T −t)
d1
=
σ ( T − t)
V
T
= The desired speed = 32.67 mph
I = The guaranteed speed = X = 32.67 mph
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-43