Indiana University  Research & Creative Activity Spring 2002 • Volume XXIV Number 3


MATH PLAYS THE MARKET

by Ceci Jones Schrock

Conjure up an image of a math professor, and what leaps to mind? A messy office dominated by blackboards filled with arcane symbols? Geeky dress shirts and pocket protectors? An intense preoccupation with an obscure subject? Then meet Indiana University Bloomington Professor Victor Goodman, a stylish man with a warm smile—not to mention a neatly appointed office with framed drawings by M. C. Escher on the wall as well as a pilot’s license. Goodman, on the IUB math faculty since 1972, is an academic pragmatist with little preference for the ivory tower.

photo of Victor Goodman
Victor Goodman is professor of mathematics at Indiana University Bloomington. photo ©2001 Tyagan Miller

“I need to be useful,” he says. “I prefer to try to use math, rather than just develop it.”

So Goodman takes mathematical and probability principles into the world of money. His research area, probability theory and its application to mathematical finance, brings together business, mathematics, statistics, and computer science to address problems arising in the world of finance.

A career direction is born

According to Goodman, investment banks, hedge funds (private investment pools much like mutual funds, except that they’re open only to institutions or very wealthy people), insurance companies, corporate treasuries, and regulatory agencies all employ the methods of mathematical finance.

In fact, the financial world has seen a boom in mathematical tools and models since the advent of the Nobel Prize–winning Black-Scholes options-pricing model in 1973. (An option is exactly what it sounds like: it gives its buyer the option, but not the obligation, to trade something at a certain price on a certain date.) Building on the Black-Scholes model, much of Goodman’s work involves discovering price relationships.

“Let’s say you have a market and a specific stock, and that stock price is jumping around all the time,” says Goodman. “Financial mathematicians seek to build a formula or a series of formulas with which you can predict how so-called options on a stock change when the stock price changes.”

With no background in business or finance, Goodman says he became interested in financial math about four or five years ago.
“I had heard that Wall Street hired lots of rocket scientists in the 1980s,” he says. “Apparently, there was this flood of high-tech people, knowledgeable physicists and so forth, going to Wall Street. I wondered what in the world they were doing there. It turns out they were pioneering this relationship between options and stock prices.”

To feed his curiosity, Goodman talked to finance professors at IU’s Kelley School of Business, and his new career direction was born.

Since then, he has collaborated with IUB math colleague Joseph Stampfli on a book, The Mathematics of Finance: Modeling and Hedging (Brooks/Cole, 2001), as well as pioneered a new option for the department’s master’s degree: the Master of Arts in Mathematics with a Specialization in the Mathematics of Finance.

Goodman becomes animated when talking about price relationships and formulas. “The really complicated problems are the ones where you’re dealing with not one stock, but with, maybe, 40 of them,” he says. “The scenario where that is really important is when you’re talking about bond markets.”

A bond, says Goodman, is a promise that you will repay a loan. “People buy and sell these bonds, and they’re all loans that are due at different times. There’s the borrower, and the other person who owns the bond, and the borrower’s promise that someday they’ll give the money back.”

Goodman says the challenge facing financial mathematicians working in the bond market is to come up with a model that allows all the bonds to have different prices, but still expresses some consistency between the prices so that brokerage firms can confidently predict options.

Wall street comes to him

But how do investment bankers and brokerage houses—the people who are really investing and manipulating money—get their hands on Goodman’s models and formulas? Does he have aspirations of working in the private sector?

“Oh, I like the laid-back academic life,” he says with a laugh. “I have the luxury to help students, so I think I’m going to resist the urge to go to Wall Street.”

That doesn’t mean he doesn’t share his work with the high rollers. Goodman tests out his models using old data. Once he is pretty confident of a model’s functionality, Goodman says he starts publicizing his findings—but not through that bastion of the academy known as the academic journal. That would be too slow.

“If my model is really hot, then I would perhaps e-mail an investment bank and say, ‘You know, I want to come talk to you about this.’ I haven’t done that part yet,” he says with a sly grin.

But he has hosted several mathematicians from big-name brokerage firms. “It’s a symbiotic relationship,” he says. “A mathematical person from a firm will come here, and we’ll spend a day talking about math questions he or she is wrestling with. I’ll try to help with what I know.”

Take, for instance, Alex Lipton from Deutsche Bank. Once a mathematician, Lipton came to Bloomington to discuss a new type of option that allows for speculation on foreign exchange currency rates.

Goodman is still waiting for Alan Greenspan to come for a visit. “Oh, that would be wonderful. That’s a fantasy.”

Master’s with many options

One fantasy that’s become a reality for Goodman is the creation of the new master’s degree option in financial mathematics. Launched in fall 2001, the degree option involves a two-year, 30-credit program.

Goodman directs the program, which includes coursework in the Department of Economics and the business school’s Department of Finance. According to its literature, the program should attract students with degrees in the mathematical, physical, and engineering sciences who wish to pursue a career in the finance industry and are prepared to develop strong analytical skills—as well as IU undergraduates who will be able to complete a combined B.A./M.A. degree in six years.
Goodman hopes the new degree option will provide students with skills that allow them to be “of use.”

“I think it’s ideal for a person to spend a brief amount of time in graduate school and to come out with valuable skills in order to pursue a good career. We know our students will be hired for their math skills and finance knowledge,” he says.

Wall Street is exactly where 24-year-old Bernardo Santos Andrade of Brazil hopes to land a job. Having grown up in a household where economics was a frequent dinner-table topic, Andrade says he has always been interested in the value of money. Completing, jointly, his doctorate in economics and the new M.A. option in financial math, Andrade is certain about his future.

“I’m sure I don’t want to be a professor,” he says. “Economists tend to focus on academic research—I want to work in the real world. This master’s degree will broaden my opportunities and allow me to apply these tools toward a job in the private sector.”

He’s not alone. According to the U.S. Department of Labor’s Bureau of Labor Statistics, employment in the securities and commodities industry is projected to rise 40 percent from 1998 to 2008, compared with the 15 percent projected for all industries in the economy.

Andrade says Goodman’s course, Introduction to the Mathematics of Finance, focuses on explaining the process of computing stock prices—but students get much more out of it. “We learn how formulas are derived, which gives us the knowledge to tweak the formula a little bit for our purposes,” he says.

Andrade praises Goodman’s teaching talents, particular his use of humor and his ability to make the content interesting.

“He knows the material from more than an academic point of view,” he says. “I don’t play the stock market, but after this class I think I will.”

By inspiring his students to take their knowledge out of the classroom, Goodman is spreading financial math to the masses.
“The master’s program exposes our students to some really good, interesting mathematics,” he says. “That’s why I study it too.”

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