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Financial Mathematics

Contacts

Office: Sequoia Hall, 390 Serra Mall
Mail Code: 94305-4065
Phone: 650.723.1796
Web Site: http://finmath.stanford.edu

The departments of Mathematics and Statistics, in close cooperation with the departments of Economics and Management Science and Engineering, and the Graduate School of Business, offer an interdisciplinary Master of Science degree in Financial Mathematics. The Financial Mathematics program provides a master's-level education in applied and computational mathematics, statistics, and financial applications.

Graduate Program in Financial Mathematics

The Financial Mathematics M.S. degree program is no longer offered through the School of Humanities and Sciences. The Institute for Computational and Mathematical Engineering (ICME) now offers a master's degree track in Mathematical and Computational Finance

Learning Outcomes (Graduate)

The purpose of the master's program is to further develop knowledge and skills in Financial Mathematics and to prepare students for a professional career or doctoral studies. This is achieved through completion of courses, in the primary field as well as related areas, and experience with independent work and specialization.

Master of Science in Financial Mathematics

Admission

New students as well as coterm students are no longer being accepted into the Financial Mathematics Program. All currently-enrolled students have the option to complete the degree within the time limits established when they were accepted into the program as detailed in the then applicable Stanford Bulletin.

Degree Prerequisites

Linear algebra at the level of:
MATH 104Applied Matrix Theory3
Real analysis (Advanced Calculus) at the level of:
MATH 115Functions of a Real Variable3
Probability at the level of:
STATS 116Theory of Probability3-5
Theory of statistics at the level of:
STATS 200Introduction to Statistical Inference3
Stochastic processes at the level of:
STATS 217Introduction to Stochastic Processes3
or MATH 136 Stochastic Processes
Computer programming at the level of:
CS 106AProgramming Methodology3-5
CS 106BProgramming Abstractions3-5

Some of these courses (e.g., STATS 116 Theory of Probability, STATS 217 Introduction to Stochastic Processes) are usually offered during the Summer Quarter so candidates lacking the required background may consider taking them then.

Degree Requirements

The program requires completion of 45 units of course work. With the advice of the faculty adviser and of peer students, each student selects his or her own set of electives and pace of study. All requirements for the Financial Mathematics master's degree must be completed within three years after the student's first term of enrollment in the master's program. Units for a given course may not be counted to meet the requirements of more than one degree, that is, no units may be double-counted. Students pursuing a coterminal master’s degree must complete their requirements within three years of their first quarter of graduate standing.

No courses taken more than two quarters prior to admission to the coterminal master’s program may be used to meet the 45-unit University minimum requirement for the master’s degree.Students who do not complete all requirements within three years of admission have their program terminated.Ordinarily, four or five quarters are needed to complete all requirements.Students must fulfill the following requirements for the M.S. degree:

1. Six courses must be taken from the list of required courses and six must be taken from the list of elective courses, available below. These courses must be taken for a letter grade, but students may elect to take one of the 12 courses for credit/no credit. An overall grade point average (GPA) of 2.75 is required. There is no thesis requirement.

2. Any remaining units required to complete the 45 total must be taken from the following options, and may be taken for a letter grade or CR/NC:

    a. Choose from the approved list of electives with emphasis on computation, information technology or finance.

    b. Choose from the following courses:

STATS 200Introduction to Statistical Inference3
STATS 217Introduction to Stochastic Processes3
STATS 218Introduction to Stochastic Processes3
MATH 131PPartial Differential Equations I3
MATH 132Partial Differential Equations II3
ECON 140Introduction to Financial Economics5

    c. Choose from CS (practical) courses; must be approved by the Program Director.

    d. In the form of an industrial internship in the Bay Area or elsewhere, with the approval and supervision of a faculty member. A written report must be submitted upon completion of the internship. Students who choose to take credit for practical training must sign up for STATS 297 Practical Training (1-3 units).

3. Submission of approved Masters Program Proposal by the Program Director to the Student Services Officer by the end of the first quarter of the master's degree program.

Required Courses

In partial fulfillment of the M.S. degree in Financial Mathematics, students must fulfill six required courses, with two from each of the following three core areas:

  1. Statistical Methods and Models
  2. Modeling, Simulation and Computing
  3. Finance

The selection of these courses is to be done in consultation with the Program Director. The following courses can be counted toward the six required courses:

Mathematics:
MATH 236Introduction to Stochastic Differential Equations3
MATH 238Mathematical Finance3
MATH 239Computation and Simulation in Finance3
Statistics:
STATS 240Statistical Methods in Finance3-4
STATS 241Econometric Modeling Methodology and Applications to Financial Markets *3-4
STATS 242Algorithmic Trading and Quantitative Strategies3
STATS 243Financial Models and Statistical Methods in Active Risk Management3-4
STATS 315AModern Applied Statistics: Learning2-3
STATS 315BModern Applied Statistics: Data Mining2-3
STATS 362Topic: Monte Carlo2-3
Management Science & Engineering:
MS&E 347Credit Risk: Modeling and Management3
Graduate School of Business:
FINANCE 622Dynamic Asset Pricing Theory4

At the Program Director's discretion, courses taken previously that are equivalent to the above may be waived; in which case they must be replaced by elective courses in the same subject area.

Elective Courses

Each candidate must take at least six approved elective courses from the list below, with two from each of the three core areas:

  1. Statistical Methods and Models
  2. Modeling, Simulation and Computing
  3. Finance

Other elective courses may be authorized by the Program Director if they provide skills relevant to financial mathematics and do not overlap with courses in the candidate's program.

Mathematics:
MATH 136Stochastic Processes3
MATH 205A/205BReal Analysis3
MATH 227Partial Differential Equations and Diffusion Processes3
MATH 256APartial Differential Equations3
MATH 261AFunctional Analysis3
MATH 266Computational Signal Processing and Wavelets3
Statistics:
STATS 202Data Mining and Analysis3
STATS 206Applied Multivariate Analysis3
STATS 207Introduction to Time Series Analysis3
STATS 212Applied Statistics with SAS3
STATS 219Stochastic Processes3
STATS 237Theory of Investment Portfolios and Derivative Securities3
STATS 238The Future of Finance2
STATS 240Statistical Methods in Finance3-4
STATS 242Algorithmic Trading and Quantitative Strategies3
STATS 243Financial Models and Statistical Methods in Active Risk Management3-4
STATS 305Introduction to Statistical Modeling3
STATS 306AMethods for Applied Statistics2-4
STATS 310A/310B/310CTheory of Probability2-4
STATS 315A/315BModern Applied Statistics: Learning2-3
STATS 317Stochastic Processes3
STATS 318Modern Markov Chains3
STATS 322Function Estimation in White Noise3
STATS 362Topic: Monte Carlo2-3
STATS 376AInformation Theory3
Computer Science:*
CS 106BProgramming Abstractions3-5
CS 106XProgramming Abstractions (Accelerated)3-5
CS 224MMulti-Agent Systems3
CS 295Software Engineering2-3
CS 229Machine Learning3-4
CS 249AObject-Oriented Programming from a Modeling and Simulation Perspective3
CS 261Optimization and Algorithmic Paradigms3
*

CS 339 may be used to fulfill this requirement; this course is offered occasionally.

Economics:
ECON 190Introduction to Financial Accounting5
ECON 202N/203N202 For Non-Economics Ph.D. Students2-5
ECON 210Core Economics: Modules 3 and 72-5
ECON 211Core Economics: Modules 11 and 122-5
ECON 275Time Series Econometrics2-5
Management Science & Engineering:
MS&E 242H
MS&E 247S3
MS&E 310Linear Programming3
MS&E 311Optimization3
MS&E 312Advanced Methods in Numerical Optimization3
MS&E 313
MS&E 322Stochastic Calculus and Control3
MS&E 342
MS&E 348Optimization of Uncertainty and Applications in Finance3
MS&E 349
MS&E 351Dynamic Programming and Stochastic Control3
MS&E 444
MS&E 445Projects in Wealth Management3-4
Graduate School of Business (GSB), Finance:
FINANCE 320Debt Markets 14
FINANCE 326Derivative Securities 14
FINANCE 327Financial Markets4
FINANCE 620Financial Markets I 13
FINANCE 621Financial Markets II 14
FINANCE 622Dynamic Asset Pricing Theory 14
FINANCE 625Empirical Asset Pricing4
Graduate School of Business (GSB), Economic Analysis and Policy:
MGTECON 600Microeconomic Analysis I 14
MGTECON 604Econometric Methods II 14
MGTECON 609Applied Econometrics and Economic Research 14
1

Indicates courses of limited enrollment and/or that instructor consent is required for registration.

For additional information about the Financial Mathematics master's degree program requirements, see the department web site.

Director: Tze Leung Lai

Steering Committee

Amir Dembo, Kay Giesecke, Tze Leung Lai, George Papanicolaou, Bala Rajaratnam, Kenneth Singleton

Core Faculty

Business: Darrell Duffie, J. Michael Harrison, Kenneth Singleton

Economics: Monika Piazzesi, Martin Schneider, John Shoven

Electrical Engineering: Stephen Boyd, Benjamin Van Roy

Institute of Computational and Mathematical Engineering: Margot Gerritsen

Management Science and Engineering: Kay Giesecke, Peter Glynn, David Luenberger, Benjamin Van Roy

Mathematics: Simon Brendle, Amir Dembo, George Papanicolaou

Statistics: Amir Dembo, David Donoho, Tze Leung Lai, Art Owen, Bala Rajaratnam