Program in Quantitative Finance

Applied Mathematics and Statistics

Stony Brook University

Sample Programs of Study

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This is intented as a guide for advisors and students to help them plan specific programs of study. We recommend that you first review the Department's general AMS Graduate Program and then the specific requirements of the Program in Quantitative Finance in Graduate Requirements. Detailed descriptions of the Quantitative Finance courses themselves can be found under Graduate Courses.


The first part reviews the overall Program in Quantitative Finance and summarizes the sequence of course prerequisites. The second part discusses three potential emphases under the general umbrella of Quantitative Finance. It is important to note that all of the sample programs of study share the same core requirements.


These emphases are not formal program elements; however, they serve to show how the Program in Quantitative Finance can be adapted to produce practitioners and researchers who have solid backgrounds in applied mathematics and finance but who also wish to develop a level of specialization in one area of the discipline. They are by no means intended to represent an exhaustive description of the range of choices available to students in the Program.


IMPORTANT: This guide is a planning document that includes courses that have not yet received approval from the Graduate School. As of the Fall 2005 semester the key program elements (AMS 511, AMS 512, AMS 513 an AMS 514) have, however, been approved.


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Basic Program and Its Prerequisites


The curriculum builds a solid mathematical foundation in the first semester. In the second semester the first core course, AMS 511 - Foundations of Quantitative Finance, is taken and the student's general mathematical development continues. In the third semester the advanced core courses are taken: AMS 512 - Capital Markets & Portfolio Theory, and AMS 513 - Financial Derivatives and Stochastic Calculus. Two highly recommended electives for all student are AMS 514 - Computational Finance and AMS 515 - Case Studies in Quantitative Finance.


The diagram below is only intended to help illustrate the prerequisites for Quantitative Finance courses. It does not represent a complete specification of the requirements for either the Masters degree or doctorate. Consult Graduate Requirements for this information.

For Masters students wishing to emphasize a particular area of finance or intending to continue on to a Ph.D. there are four advanced courses that can prepare him or her to begin research work: AMS 516 - Advanced Portfolio Optimization, AMS 517 - Advanced Options Theory and Valuation, AMS 518 - Interest Rate Securities Theory and Valuation. and AMS 519 - Crdit Risk Modeling and Credit Derivatives. The usual special topics course, AMS 691 - Special Topics (Quantitative Finance), rounds out the options available to advanced students.

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Program Emphases


Three potential areas of specialization within Quantitative Finance are considered:


  • Portfolio Management: dealing with issues of risk control, portfolio construction, and general investment management,
  • Financial Engineering: covering the construction and pricing of derivative products for return enhancement and hedging, and
  • Computational Finance: focusing on financial decision making and pricing requiring the application of advanced numerical programming techniques


Users of this page should also consult the Career Guide which describes several possible career paths in Quantitative Finance. This is an interdiscinplinary field and, for example, the creation of a large investment portfolio may well reguire a team of professionals who, although they share a common background in applied mathematics, specialize in areas such as optimization, statistical estimation, economic analysis, risk control, derivatives pricing and so forth.

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Portfolio Management Emphasis


Financial resources must be managed in the face of uncertain investmemt performance and future consumption. The risk and reward of available investments must be modeled and estimated. These insights must then be translated into a set of specific investment decisions. All of this must be done in the context of the objectives and constraints imposed by both the organization and the larger legal and economic environment it finds itself in.


A Master’s student wishing to emphasize portfolio management within the Quantitative Finance Track would take a sequence including AMS 576 - Statistical Methods for the Social Sciences and AMS - 505 Applied Linear Algebra terminating in AMS 516 - Advanced Portfolio Optimization. Other elelctives chosen from within the Department would focus on the areas of optimization theory and statistical estimation.


A more serious student contemplating a PhD would take the sequence AMS 570 - and AMS 571 - Mathematical Statistics I and II instead of AMS 576 - Statistical Methods for the Social Sciences and would also take AMS 544 - Nonlinear and Discrete Optimization and then be ready to take AMS 516 - Advanced Portfolio Optimization in his or her fourth semester.

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Financial Engineering Emphasis


A derivative is a financial instrument whose value is a function of the price of one or more underlying financial instruments or on one or more economic factors, for example an option to buy a stock at some future date at some fixed price or a swap of a payment based on a fixed rate for one based on a variable one. There is also a class of financial instruments called collateralized obligations which separate the cash flows of a pool of obligations such as credit card debt or mortgages into separate streams having different characteristics. These financial products break down the risk and reward components of a security that so they can be reallocated more efficiently in the market.


A Master’s student wishing to emphasize financial engineering within the Quantitative Finance Track would take a sequence terminating in AMS 517 - Advanced Options Theory. Other electives chosen from within the Department would focus on the areas of stochastic processes, differential equations and numerical analysis.


A more serious student contemplating a Ph.D. would take the sequence AMS 570 - and AMS 571 - Mathematical Statistics I and II instead of AMS 576 - Statistical Methods for the Social Sciences and would be ready to take AMS 517 - Advanced Options Theory.

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Computational Finance Emphasis


The class of problems in applied mathematics that we can solve using computer-based numerical methods is far larger than the one for which we have direct analytical solutions. In financial markets, the firm that can price an exotic instrument, optimize a complex portfolio, estimate the risks of a set of financial positions or simulate a range of economic scenarios more quickly or accurately than other firms has a tremendous competitive advantage.


A Master’s student wishing to emphasize computational finance within the Quantitative Finance Track would start out taking the usual sequence of courses. Electives would include AMS 514 - Computational Finance plus additional electives from withing the Department in mathematical programming, numerical analysis and computer science.


A more serious student contemplating a Ph.D. would work closely with other students and faculty working in Computational Mathematics. Although all of the courses within Quantitative Finance involve some programming components, students in wishing to emphasize this area would be expected to develop strong programming skills, including a knowledge of parallel computing.

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