Math Programs Put Students On Fast Track To Wall Street

March 8, 1998

David Shaw (left), chairman of D.E. Shaw & Co. and guest speaker at a reception for the new Courant program in financial mathematics, with Neil Chriss of Morgan Stanley & Co., who is also director of the Courant program.
It's no secret that a lot of scientists have left academic careers to go to Wall Street, says Robert Almgren of the University of Chicago, "and that's a waste for everyone." As associate director of Chicago's new professional master's degree program in financial mathematics, Almgren clearly has no problem with mathematicians who work on Wall Street; it's the path they take to get there that concerns him.

Students today are more informed about their choices at a much earlier point, Almgren believes. Smart students interested in working in the financial industry "see up front that what they need to know can be gotten in a one- or two-year master's program."

Within the last few years, mathematics departments at several universities have introduced professional master's degree programs in financial mathematics. Joining forces in an effort to bring the new programs to the attention of both the industry and other universities, three of the programs--at Chicago, Columbia University, and the Courant Institute of Mathematical Sciences, New York University--have founded the Association of Financial Mathematics Programs.

Representatives of all three programs, outnumbered many times over by Wall Street professionals, were on hand on December 2 for a reception held in New York to announce the creation of the newest of the programs--Courant's master of science program in the mathematics of finance. Guest speaker David Shaw, chairman of D.E. Shaw & Co., Inc.--"the most intriguing and mysterious force on Wall Street today," according to Fortune magazine--surveyed quantitative methods in finance, touching on both obvious and nonobvious applications and giving a glimpse of the philosophy of his nine-year-old investment banking firm. D.E. Shaw's niche, Shaw told the audience, is in finding "interesting ways of applying computation to finance." Looking forward to "enormous contributions" from the Courant program to the industry, Shaw also cited an urgent need on the public-sector side to understand and regulate techniques: "I would be disappointed if some graduates of the program didn't go to work for regulatory agencies or on Capitol Hill."

The Chicago/Columbia/Courant association was founded in large part to make potential employers of the financial mathematics graduates aware of the programs, and to establish curriculum guidelines so that employers would know what could be expected of graduates. The association also hopes to offer guidance to other mathematics departments interested in starting similar programs.

University of Chicago
Algebraist Niels Nygaard, with advice from a diverse collection of Chicago finance professionals, designed the master's degree program in the mathematics of finance that was introduced at the University of Chicago in the fall of 1996. The program has three tracks: mathematics; stochastics and economics; and financial applications, taught by industry practitioners. Of the 18 graduates who received degrees in 1997, three went on to PhD programs in finance or economics, and the other 15 are working at international commercial banks, hedge funds, investment banks, and consulting companies.

"We think that the employment picture for the future looks very good," Nygaard says, "and we foresee an increasing demand for people with the kind of strong mathematical background that our program provides." Approximately 25 students will graduate this year, he says, and the plan is to keep the number of graduates between 25 and 30 in the future. Also very optimistic about the future for Chicago graduates is Jack Mosevich, a senior partner at Harris Investment Management in Chicago and one of the industry lecturers in the Chicago program. Beyond derivative pricing, he explains, the skills of these graduates will be increasingly required in two other major areas: risk management and quantitative investment, where mathematical models are used to make decisions.

A former professor of mathematics, Mosevich got interested in the markets about 12 years ago, "right about when they started using more mathematics." Hired as a "quant," on the bond desk at Merrill Lynch, he is enthusiastic about the environment in which he has worked ever since: "What I like about the industry is that it's one of the areas where you can use your mathematics--and it's not trivial mathematics--and still be doing industrial work." "Employment prospects seem to be healthy," he says, "but there's another angle: People shouldn't go into this just for the money." Referring again to the "wonderful mathematics research" being done in the area of financial mathematics, he cites modeling the stochastic properties of interest rates and the behavior of asset prices as just a few examples of big unsolved problems.

Asked about the existence of a professional master's degree program in an extremely research-oriented department, Nygaard echoes Mosevich: "The kind of problems arising from quantitative finance in the industry today has scientific merit and makes for interesting problems for applied mathematicians to consider."

Robert Almgren, an assistant professor of mathematics who teaches linear algebra and numerical methods for PDEs in the program's mathematics sequence, considers financial mathematics a natural outgrowth of his work in applied mathematics and free boundary problems. Recently, with Neil Chriss (director of the Courant program), Almgren wrote his first financial mathematics paper, on optimal liquidation strategies; as always, Almgren comments, the trick is in choosing the right problem, in developing a realistic model that can be solved.

Describing the students in the mathematics courses as motivated, sharp, and interesting, Almgren emphasizes that the mathematics taught in the programs at all three universities is high-level mathematics. "The intellectual level is the same as in the first year of our PhD programs," he says, adding that he teaches the financial mathematics courses from a different perspective. "The students won't have years and years to go back over the material. If they don't understand it as you teach it, they let you know."

In December and again in January, Almgren and Nygaard visited investment banks in London, both to inform them about the new program and to learn more about the kinds of people the banks were looking to hire. Several of the banks indicated that they would plan to interview financial master's students along with MBAs on their regular recruiting trips to Chicago. One other result of the visits is a very possible change in the Chicago program on its three-year anniversary: the addition of a thesis requirement, and a consequent expansion of the program to two years.

Paul Kornfeld, who works on the equities trading desk at EBF and Associates, received a master's degree from the Chicago program in 1997. Having graduated from Chicago in 1996 with a BS/MS in mathematics and an interest in probability theory, he went straight into the program, which he describes as challenging and to which he unequivocally attributes his current employment.

"The job is more than just knowing math," he says, "it's knowing the subject you're modeling." Someone with a PhD in mathematics or physics might have more extensive knowledge of the methods, he continues; what the program provides is an introduction to finance, to what actually needs to be done in the industry.

In developing models at EBF, Kornfeld works closely with traders, who provide a lot of inputs, including their intuition, to the models. "You can't learn about doing that from books," he says. An especially valuable part of the program for Kornfeld was an internship at Morgan Stanley, where, under the supervision of Neil Chriss, he worked with another intern on a family of models used to predict the volatility of assets. The project, which included researching the subject and developing a set of Matlab routines, culminated with a presentation to professionals at Morgan Stanley.

Columbia University
In the fall of 1997, the Department of Mathematics at Columbia welcomed into its master of arts in mathematics program the first 14 students specializing in the mathematics of finance. Ioannis Karatzas, Higgins Professor of Applied Probability at Columbia, is director of the financial mathematics program.

The program, which is co-sponsored by the Department of Statistics, draws on the university's strengths in stochastics, numerical methods, and applications of finance, including portfolio analysis, option pricing, and interest rate modeling. Courses include Introduction to the Mathematics of Finance, Stochastic Processes, Statistical Inference and Time-Series Modeling, Stochastic Methods in Finance, and Numerical Methods in Finance; also offered are a practitioners' seminar and three electives (with topics including numerical methods for PDEs, advanced microeconomic analysis, and topics in the mathematics of finance).

As at Chicago, Columbia students can complete the program in one year of full-time study; part-time students can complete the requirements in three or more semesters. All required courses are given in the evening. Important components of the program are the weekly seminar, conducted by practitioners from industry, who discuss their work, give mini-courses, and present open problems, and the two-day Columbia–JAFEE Conference on the Mathematics of Finance, held each year in early April. The seminars and the conference provide opportunities for students to interact both with industry practitioners and with academics from outside Columbia.

Students in one fall-semester course taught by Mikhail Smirnov completed a variety of assigned projects, in some cases, he says, turning in outstanding work. Project topics included the development of computer models to calculate prices and sensitivities of various nonstandard trading options; the application of high-speed Monte Carlo methods to exotic options; in-depth study of certain sovereign bond markets and the opportunities they present; the numerical solution of a nonstandard boundary value problem for Black–Scholes; and the study of alternatives to Black–Scholes models.

Requirements for admission to the program are a "very substantial background in mathematics," at the level of an undergraduate major in mathematics, physics, or some other discipline in science or engineering. The students in the first group vary considerably in background-a good thing, according to Karatzas, who sees the students learning "about as much from each other as they do from the professors who teach their classes." A few of the students in the first group have PhDs in mathematics; others have bachelor's or master's degrees in physics or engineering or backgrounds in economics or finance, and a few have some work experience.

Paul Zhao, sector manager of the treasury and agency components of three total rate-of-return bond accounts at TIAA–CREF, is a part-time student in the Columbia program. With a master's degree from the Yale School of Management, he was looking for more rigorous mathematical skills after business school. The courses at Columbia are challenging, he says, and are providing the technical skills that "are becoming more and more critical to an understanding of the fixed-income markets." Zhao, who has also worked on a derivative hedging program and on risk management in his 20 months at TIAA–CREF, views the program as useful to any quantitative portfolio manager.

Darren Clipston entered the Columbia program with degrees in electrical engineering and commerce from the University of Western Australia, along with two and a half years of experience as a financial analyst with an Australian Merchant Bank. Interested fundamentally "in applying clever methodologies and a measure of creativity to solving real financial problems," he was looking for an "intense, relatively short program" that would bring him up to speed on the latest pricing and modeling techniques.

After graduation, Clipston would like to work in the analysis and trading of derivatives or fixed-income securities. Assessing the current job market for highly skilled financial professionals as fairly strong, he believes that "the best opportunities are available to persons with skills immediately applicable in the key businesses of investment banks and other financial firms."

In developing the courses for the program, Clipston believes, Columbia faculty had "a keen eye on the skills most in demand on Wall Street. . . . I have seen many examples in the markets where professionals with incrementally better understanding of the processes driving transactions capture significant returns from these insights. Compared with the many alternatives I considered for graduate studies, this program offers the best way to gain such insights within a reasonable time frame. It is a tough workload but a great challenge at the same time."

Courant Institute
Part-time students with jobs on Wall Street will always account for a large part of the enrollment in Courant's new master's degree program in financial mathematics, says Courant deputy director Robert Kohn. In fact, he points out, it was inquiries from just such students, "looking for a viewpoint on finance that they could get from us, different from what they could get in the business school," that led Courant faculty about three years ago to create the first of the eight new courses now offered as part of the new program.

Key faculty in the Courant program---Marco Avellaneda (at podium), program director Neil Chriss, Jonathan Goodman, and Robert Kohn---at the December reception. "This program," says Chriss, "offers Wall Street what it doesn't presently have: a reliable stream of mathematical talent, specifically educated for careers in finance."

A full-year course in mathematical finance, developed and first taught by Marco Avellaneda in 1995, has become the theoretical core of the program. A one-semester course on computational methods in finance developed by Jonathan Goodman at about the same time, together with an existing master's-level course in scientific computing, forms the computational core of the program. (It was also at that time that, extending Courant's longstanding ties with the financial industry, Avellaneda introduced Courant's research seminars in mathematical finance--a series of lectures, about eight per semester, given and attended by academics and industry professionals in the New York area.)

Courant program director Neil Chriss, one of the many PhD mathematicians now working on Wall Street (in equity risk management at Morgan Stanley), not surprisingly points to "a very high level of industry contact" as one of the most important characteristics of the program. Given Courant's strengths in PDEs, stochastic processes, computational methods--"exactly the mathematics used on Wall Street"--and its geographic location, Chriss anticipates the active participation in the program of derivative traders, risk managers, hedge fund operators, and people from regulatory agencies and a wide variety of related environments. Top people from Wall Street (loosely defined), he says, have expressed interest both in becoming members of the new program's advisory board and in teaching in the applications component of the program.

The students who come in to this program, Chriss says, have to learn serious mathematical and computational techniques; at the same time they need to learn what actually goes on in the industry. Students who interview at firms like Morgan Stanley and Goldman Sachs "need to be really smart and technically good; they also need to be able to fit into the firms culturally--that's what they'll get through their exposure to the faculty from Wall Street."

As Kohn points out, many of the Courant students are already working in the financial industry--"our classrooms are filled half with suits, half with blue jeans"--and courses are offered in the evening to accommodate those with full-time jobs. One such student is Kevin Boyle, who expects to receive a master's degree in financial mathematics in May. A computer consultant in fixed-income risk management at Sanwa Financial Products, Boyle has been a part-time student at Courant, on and off, for about three years. Initially working toward an MS in pure mathematics, he later realized that an applied mathematics program would be of greater benefit to his career and switched to the program in financial mathematics. Especially enthusiastic about a course on equity risk management taught by Peter Fraenkel of Morgan Stanley, Boyle hopes, with the deeper understanding of financial markets that he has acquired at Courant, to continue in fixed-income risk management.

Mathematics students at Courant have been studying finance for some time, at both the MS and the PhD level, says Kohn, pointing out that increasing numbers of these students, as well as Courant postdocs, have been pursuing careers in the finance industry--"roughly 10% of finishing Courant PhDs over the last five years, and three of 14 in 1996–97, took first jobs there."

Among those studying financial mathematics in more traditional Courant programs is Stephanie Curcuru, who has almost completed the requirements for an MS in applied mathematics. With a BS in aerospace engineering (1990), Curcuru was working at Price Waterhouse as a manufacturing consultant when the company began to seek out people with mathematics backgrounds to develop derivative products. Hooked on the "wildly exciting and unpredictable financial markets," she moved four years ago to the fixed-income trading desk at Salomon Brothers. "I've taken programs--optimization programs, for example--that I wrote in my classes and have been able to use them immediately in my work," she says.

Tim Glauner, a programmer in fixed-income derivatives at CDC Capital, would like "to move more to the quantitative side, to become a more sophisticated programmer, eventually moving into financial engineering." With bachelor's and master's degrees in computer science, he is working part-time toward an MS in mathematics (and possibly at some point a PhD) at Courant, taking pure mathematics courses as well as both semesters of the financial mathematics class. Looking for "a deeper and more structured understanding of financial markets," he is at Courant to "get the mathematics background that lets you learn on the job."

"Financial mathematics," says Kohn, "is a legitimate branch of applied mathematics. It involves modeling, simulation, comparison between the models and real data, and all the other hallmarks of our field. And it offers challenging career opportunities for bright people at all levels.

"The present growth of interest in various mathematics departments is not a fad," he continues; "rather, the applied math community is finally waking up to an intellectual and pedagogical opportunity we should have noticed long ago."

"We're looking to change the way banks look at quants," Chriss says; "I think these people will increasingly be in demand." Expectations for them will increase as well, he believes. People with master's degrees in mathematical finance may be less specialized than someone with a PhD in mathematics, but they will know a lot about the business going in."

SIAM plans to gather and disseminate information about the many existing programs in financial mathematics to the mathematical sciences community and encourages readers to submit any available information to executive director James M. Crowley (

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