# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"A Calculus of Risk," by Gary Stix. *Scientific American*, May 1998.

As worldwide financial markets become more interconnected and complex,new investment products have emerged that can provide insurance against risk, like a drop in the yen or in the thermometer. The act of pricing uncertainty, in the form of derivatives and options, is theessence of financial engineering, an emerging field that is bringing mathematicians, physicists, and computer scientists to WallStreet.

Academics such as Louis Bachelier and Albert Einstein contributed to the theory of finance early in this century, but it did not catch firewith investors until the early 1970s, when the Black-Scholes equationsturned the difficult problem of options-pricing into an operation that can be performed on a pocket calculator. However, behind Black-Scholes is stochastic calculus, so enter the Wall Street "rocketscientists" who use this complicated math to develop models thatbuild upon Black-Scholes. Hundreds of mathematical models arecurrently in use to optimize options-pricing strategy.

No mathematical model can capture the multitude of ever-changing economic factors that perturb world markets. Modeling problemshave led to billions of dollars in derivatives losses, and some economists wonder if these models can match the skill andintuition of traders. Emanuel Derman of Golman Sachs, a proponentof modeling, counters with the philosophy that we should"let 1000 models bloom"--the more models we investigate, thebetter we will bridge the gap between models and the real world.

Despite the concerns of some, financial engineering hasflourished on Wall Street, and its influence is spreading. Dermanspeculates that the Black-Scholes model could be used to organizethe financial lives of people in general, in an attempt to hedgewhatever risks we may encounter.*--- Ben Stein*