Mathematics Provides Tools for Financial Decisionmaking
The use of mathematics is becoming mandatory when it comes to the world of
finance. "
Optional Mathematics is Not Optional
" is the message and title of an
article by John Price, to be published in the September 1996 issue of the
Notices of the AMS. Price, Professor of Mathematics at Maharishi University of
Management, has consulted for major banks, government departments, and
investment companies in the U.S. and Australia.
"Financial debacles such as Orange County, Barings Bank, and others have left
corporate America and the government nervous about financial risk," says
Price. "Gone are the days of managing risk through flying by the seat of your
pants. Treasurers and risk managers need to take a more systematic approach
using mathematics to implement prudent stratagies to maximize their profits
while protecting against unexpected losses."
For example, suppose that, to plan for its future, an airline would like to
insure that its fuel prices will not rise more than 5% in the next 2 years.
The airline could purchase what is known as an "option" to buy fuel at no more
than 5% above the price at the start of the 2-year period. This way, the
airline insures against the risk that the price of fuel will go up more than it
can pay.
As financial markets have exploded with options on a dizzying variety of
items---fuel, agricultural products, foreign currencies, mutual funds---options
no longer simply provide insurance against risk. They have become financial
instruments traded on the market. Mathematics can help analysts address the
important question, How can one tell if an option is over- or under-valued?
The ground-breaking 1973 paper of Fischer Black and Myron Scholes established a
mathematical model for determining the price of an option. Later work by
others on what has become known as the "binomial method" made the theory of
options pricing more widely accessible. Although numerous refinements have
been introduced, the original approach of Black and Scholes has proven hard to
beat.
Black and Scholes had the ingenious idea of adapting mathematical machinery
used in physics to the problem of options pricing. Specifically, they relied
on the mathematics of Brownian motion, the random, jostling movement of gas
molecules circulating in a closed chamber. The positions of the molecules are
determined by the small nudges they get as they bump against each other. In
much the same way, financial markets are driven by small upward and downward
nudges that occur through buying and selling.
Professor Price's article discusses the Black-Scholes model as well as some
state-of-the-art developments in the field.
-Allyn Jackson
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