Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Step 3 – Evaluate the Change that Affects Unreliability
A. Estimate the expected reduction in speed variability achieved through the implementation
of the strategy.
B. Calculate the certainty-equivalent value for the new scenario.
Step 3 – Evaluate the Change that Affects Unreliability
A. “Smart” systems, including collision-warning systems and systems that
automatically adjust cruise-control speed based on the relative distance of
the car ahead, can reduce speed variability and travel-time unreliability as
they are widely adapted in vehicles. It is estimated that the new system
would reduce the speed variability,α, by 50%.
Assumptions for the new scenario:
• Vehicle volume remains constant over time
• Unknown speed ( V T ) = 32.67 mph
• Guaranteed speed (I) = 32.67 mph
• α = 0.5×
0.3635 = 0.1817
B. The European Put option and a 5.00% risk-free interest rate are chosen.
Thus, r = 0.05
The lowest 1% speed is now 20.18 mph due to the change in the travel-time
variability. Therefore, the new contract length is given by
⎛ 60 / 20.18 ⎞
T -t
= ⎜
⎟×
10 = 0.0000566 years
⎝365× 24×
60 ⎠
Sigma 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 0.1817
σ = = = 24.17
T − t 0.0000566
Perform intermediate and final option value calculation:
2
ln( VT
/ I) + ( r+ σ / 2)( T −t)
d1
=
σ ( T − t)
2
⎛32.67 ⎞ ⎡ ⎛24.17
⎞⎤
ln ⎜ ⎟ + ⎢0.05 + ⎜ ⎟⎥
× 0.0000566
⎝32.67 ⎠ ⎝ 2 ⎠
=
⎣
⎦
= 0.09089
24.17×
0.0000566
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-45