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Master of Science in Financial Mathematics

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Financial Mathematics

Admission—To be eligible for admission, students are expected to have taken the following courses or their equivalent:

  1. Linear algebra at the level of MATH 104.
  2. Advanced calculus (real analysis) at the level of MATH 115.
  3. Basic ordinary and partial differential equations at the level of MATH 131 and 132 (basic partial differential equations).
  4. Probability at the level of STATS 116; theory of statistics at the level of STATS 200; and stochastic processes at the level of STATS 217 or, preferably, MATH 136/STATS 219.
  5. Computer programming at the level of CS 106A,B,or X.

Some of these courses are offered as summer courses and may be taken by candidates lacking the required background.

Candidates for admission must take the general Graduate Record Examination and preferably the subject test in Mathematics as well. Information about these exams can be found at http://www.gre.org.

Requirements—The program requires that the student take 45 units of work. Of these 45 units, six courses must be taken from the list of required courses and six must be taken from the list of elective courses, available on the program web site at http://finmath.stanford.edu/academics/required.html and http://finmath.stanford.edu/academics/electives.html. These courses must be taken for a letter grade, but students may elect to take one of the 12 courses credit/no credit. An overall grade point average (GPA) of 2.75 is required. A seminar in Financial Mathematics is an integral part of the program and an opportunity to interact with leading academic and industry speakers (for credit, enroll in STATS 239AB). There is no thesis requirement.

Any remaining units required to complete the 45 total must be taken from the following options:

  1. from the approved list of electives with emphasis on computation, information technology, or finance
  2. STATS 200, STATS 217, STATS 218, MATH 131, MATH 132, MATH 202 or ECON 140
  3. additional (practical) CS courses
  4. 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 (1-3 units).

Ordinarily, four quarters are needed to complete all requirements.

Required Courses—For the M.S. degree in Financial Mathematics, students must fulfill six of the following required courses:

  1. In stochastic processes and statistics:
    1. MATH 236. Introduction to Stochastic Differential Equations
    2. STATS 241. Financial Modeling and Risk Management
  2. In differential equations, simulation, and computing:
    1. MATH 227. Partial Differential Equations and Diffusion Processes

      or STATS 362. Monte Carlo Sampling

    2. MATH 239. Computation and Simulation in Finance
  3. In finance and economics:
    1. MS&E 347. Credit Risk: Modeling and Management

      or MATH 240. Topics in Financial Mathematics: Fixed Income Models

    2. MATH 238/STATS 250. Mathematical Finance

Courses that are equivalent to the above and have been taken previously may be waived by the adviser, in which case they must be replaced by elective courses in the same subject area.

The requirements must be met within two years of entering the program, or four academic quarters for those already at Stanford.

Elective Courses—Each candidate must take at least six approved elective courses from the list below.

  1. At least two electives in Probability, Stochastic Processes or Statistics from:

    Statistics:

    STATS 202. Data Analysis

    STATS 206. Applied Multivariate Analysis

    STATS 207. Introduction to Time Series Analysis

    STATS 219. Stochastic Processes (Same as MATH 136)

    STATS 220. Continuous Time Stochastic Control

    STATS 237. Time Series Modeling and Forecasting

    STATS 240. Statistical Methods in Finance

    STATS 252. Data Mining and Electronic Business

    STATS 305. Introduction to Statistical Modeling

    STATS 306A. Methods for Applied Statistics

    STATS 310A/B/C. Theory of Probability

    STATS 315A/B/C. Modern Applied Statistics

    STATS 317. Stochastic Processes

    STATS 318. Modern Markov Chains

    STATS 324. Multivariate and Random Matrix Theory

    STATS 343. Time Series Analysis

    EE 376A. Information Theory

    Mathematics:

    MATH 136. Stochastic Processes (Same as STATS 219)

    MATH 205A/B. Real Analysis

    MATH 237. Stochastic Equations and Random Media

    Economics:

    ECON 275. Time Series Econometrics

  2. At least two electives in Differential Equations, Optimization, Simulation, or Computing from:

    Mathematics:

    MATH 220. PDE of Applied Mathematics

    MATH 222A. Computational Methods for Fronts, Interfaces, and Waves

    MATH 256A,B. Partial Differential Equations

    MATH 261A,B. Functional Analysis

    MATH 266. Time Frequency Analysis and Wavelets

    Statistics:

    STATS 212. Applied Statistics with SAS

    STATS 227. Statistical Computing

    STATS 235. Decision Making in Financial Services

    STATS 322. Function Estimation in White Noise

    Computer Science:

    CS 106B. Programming Abstractions

    CS 106X. Programming Abstractions (Accelerated)

    CS 193D. C++

    CS 229. Machine Learning

    CS 249A. Object-Oriented Programming: A Modeling and Simulation Perspective

    CS 261. Optimization and Algorithmic Paradigms

    CS 339. Topics in Numerical Analysis

    CS 365. Randomized Algorithms

    Management Science and Engineering:

    MS&E310. Linear Programming

    MS&E 311. Optimization

    MS&E 312. Advanced Methods in Numerical Optimization

    MS&E 313. Vector Space Optimization

    MS&E 323. Simulation Theory

    MS&E 339. Approximate Dynamic Programming

    MS&E 348. Optimization of Uncertainty and Applications in Finance

    MS&E 351. Dynamic Programming and Stochastic Control

    Computational and Mathematical Engineering:

    CME 340. Computational Methods in Data Mining

    Graduate School of Business:

    OIT 667. Revenue Management*

  3. At least two electives in Economics or Finance from:

    Economics:

    ECON 202N-203N. Core Economics: Modules 1 and 2, 5 and 6 (for non-Economics Ph.D. students)

    ECON 210. Core Economics: Modules 3 and 7

    ECON 211. Core Economics: Modules 11 and 12

    ECON 269. International Financial Markets and Monetary Institutions

    ECON 281. Economics of Uncertainty

    ECON 284. Topics in Dynamic Economics

    Mathematics:

    MATH 180. Introduction to Financial Mathematics

    Statistics:

    STATS 243. Introduction to Mathematical Finance (summer version of MATH 180)

    Management Science and Engineering:

    MS&E 242H. Investment Science Honors

    MS&E 247G. International Financial Management (Same as GSB F323)*

    MS&E 247S. International Investments

    MS&E 272. Entrepreneurial Finance

    MS&E 341. Advanced Economic Analysis

    MS&E 342. Advanced Investment Science

    MS&E 345. Advanced Topics in Financial Engineering

    MS&E 444. Investment Practice*

    MS&E 445. Projects in Wealth Management

    Graduate School of Business:

    GSB F320. Debt Markets*

    GSB F326. Derivative Securities*

    GSB F328. Portfolio Management*

    GSB F620. Financial Markets I*

    GSB F621. Financial Markets II*

    GSB F622. Dynamic Asset Pricing Theory*

    GSB F629. Tax and Finance Seminar*

    MGTECON 600. Microeconomic Analysis*

    MGTECON 604. Advanced Econometrics*

    MGTECON 609. Applied Econometric and Economics Research*

*indicates courses of limited enrollment and/or that instructor's preapproval is needed for registration.

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.

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