Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Comment #6:
The original option model was developed to determine the price of traded financial options such as
call options which give the right to buy shares of common stock at a fixed price in the future or put
options which confer the right to sell shares of common stock at a fixed price in the future. The
classic derivation depends on the ability to form so-called arbitrage portfolios of traded securities
that hedge out the stochastic component of the prices. In the Black-Scholes case the other key
assumption is that the markets are complete which roughly means that traded securities can span the
uncertainty. The original option pricing model has been extended along different dimensions in a
variety of ways. For example, it has been modified to handle different stochastic assumptions
regarding the underlying securities and deal with complicated derivative structures. In addition the
range of application has been extended to value real options, such as the option a mining firm has to
open or close a mine. It has also been applied to value certain features of insurance contracts.
However in this case, successful applications relate to the valuation of embedded financial options in
insurance and annuity contracts rather than the basic insurance per se. For example, a policyholder
under an equity indexed annuity may participate in the upward moves of the S & P 500 Index and
also benefit from downside protection in case the market value falls below his initial investment.
These features are routinely valued using a combination of call and put options on the S & P Index.
A standard insurance contract such as a reinsurance policy on a house has a payout that resembles
the payout on a put option. In the case of the fire insurance contract, the premium is paid up front
and the benefit is equal to the fire damage if any. The fire damage can be viewed as the difference
between the value of the house before the fire minus the value after the fire. In the case of a
European put option on a financial security, the investor pays the option premium at inception and
receives a benefit equal to the difference between the option strike price and the market price of the
security when the option matures. While the two contracts are similar in some aspects, they are
priced in different ways using very different paradigms. The insurance contracts are priced by
actuarial methods that are based on historical statistics and underwriting. The put option is priced
using a Black Scholes type model.
Response #6:
Real-world contracts (mortgages, insurance, options on tradable securities, etc.) have features that
do, indeed, complicate the valuation exercise. However, it has long been recognized that an
insurance contract is fundamentally a put option. Actuarial complexities arise because of the need to
measure such things as the distribution of life expectancy, accident rates, etc. and to consider and
contain adverse selection distortions. Our modeling of the value of insurance against traveling
slower than the expected speed is focused on determining the underlying value of such insurance if it
existed. We are NOT modeling how rates would be set if I were imagining starting a commute-trip
insurance business. It is the underlying value of the risk (not the operating challenges of insurers,
etc.) that is of interest.
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-36