Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
• An example of an application of a European Option is in commodity trading. Here
individuals are buying the right to purchase or sell an asset at a contracted price at the
end of the contract period. Trading in commodity futures is of the European option type,
because people buy the right to purchase/sell wheat, corn, or other products at a
specified (strike) price in the future.
• Buying the right to purchase or sell an asset at a contracted price at any time during the
contract period is an American Option. Insurance policies are a type of American
Option, since the commodity being traded (money value of insured object) can be called
or put at any time during the policy coverage.
Economists have expanded the notion of options beyond financial instruments to so-called "real"
options. Real options involve the analysis of quantities such as commodities and time. Formulae
have been developed to compute the value of various types of real options under a wide range of
conditions. Many real-world insurance policies insure such real outcomes as a policy that insures
that a communications satellite will function at a specified level of performance, or for a specified
number of years. Application of options theory to travel-time reliability constitutes one
formulation of a real option.
Practitioners and experts in the real options branch of financial analysis have a very specific
meaning for the term ‘real option.’ Usually, the term refers to real assets in the capital budget
context. Since we know of no one else who has studied travel time reliability using the options
approach, it is not clear what the exact proper terminology is to use. However, Professor Lenos
Trigeorgis, a well-known expert in the field of real options, has applied the real options terms in an
analogous setting: a decision to increase flexibility of production processes as defense against
exchange rate variability. Therefore, the term ‘real option’ is used in a liberal sense for our options
theoretic approach for the valuation of travel time reliability since our certainty-equivalent
measure is easily converted to minutes (time).
Application of Black-Scholes type options formulae to non-financial options has to respect certain
underlying assumptions of the Black-Scholes model. Analysts should apply Black-Scholes to real
options in circumstances in which they make the most logical sense. A full discussion of the
underlying assumptions of Black-Scholes type option pricing models and their implications in the
development of real options such as those presented here can be found in Kodukula and Papudesu
(2006).
Because real options are not traded in a formal market, the so-called arbitrage assumption is
commonly highlighted as a limitation on the applicability of Black-Scholes to real options.
However, as Kodukula and Papudesu (p. 84) point out:
We believe that a categorical denial of the validity of the models to real option
problem is inappropriate and that a “no arbitrage” condition is only a limitation of
the model and can be overcome easily by proper adjustment. Practitioners have
used three different types of adjustment:
1. Use an interest rate that is slightly higher than the riskless rate in the option
pricing model.
2. Use a higher discount rate in calculating the discounted cash flow (DCF)
value of the underlying asset.
3. Apply an “illiquidity” discount factor to the final option value.
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-5