MS in Mathematical Finance Curriculum

The MS in Mathematical Finance (MSMF) is a full time, three semester, 36 credit program with a common core during the first semester.  In the two remaining semesters, students have the choice to concentrate in Asset Management, Quantitative Analytics, Risk Management, or Analytics & Research.

Core Curriculum

Fall Semester – 12 credits

  • MF702 Fundamentals of Finance (core, required for all students except for those planning to enroll in the Analytics & Research concentration)
  • MF703 C++ Programming for Mathematical Finance (core)
  • MF793 Statistical Methods of Mathematical Finance (core)
  • MF795 Stochastic Methods for Mathematical Finance (core)
  • FE918 Doctoral Seminar in Finance (core, only required for students planning to enroll in the Analytics & Research concentration)


Asset Management

Fall Semester – 12 credits

  • Core curriculum

Spring Semester – 12 credits

  • MF728 Fixed Income Securities (core)
  • FE825 Advanced Investments (required elective)
  • MF840 Data Analysis and Empirical Methods (required elective)
  • Elective – Choose 1 from the following list:
    • MF821 Algorithmic and High-Frequency Trading (elective)
    • MF796 Computational Methods of Mathematical Finance (elective)

Summer Semester

  • Optional internship

Fall Semester 2nd Year –12 credits

  • MF730 Portfolio Theory (required elective)
  • MF805 Empirical Asset Pricing and Portfolio Construction (required elective)
  • Electives – Choose 2 from the following list:
    • MF731 Corporate Risk Management (elective)
    • MF770 Advanced Derivatives (elective)
    • MF772 Credit Risk (elective)


Quantitative Analytics

Fall Semester – 12 credits

  • Core curriculum

Spring Semester – 12 credits

  • MF728 Fixed Income Securities (core)
  • MF794 Stochastic Optimal Control and Investment (required elective)
  • MF796 Computational Methods of Mathematical Finance (required elective)
  • MF821 Algorithmic and High-Frequency Trading (required elective)

Summer Semester

  • Optional internship

Fall Semester 2nd Year – 12 credits

  • MF730 Portfolio Theory (required elective)
  • MF770 Advanced Derivatives (required elective)
  • MF772 Credit Risk (required elective)
  • MF850 Advanced Computational Methods (required elective)


Risk Management

Fall Semester – 12 credits

  • Core curriculum

Spring Semester – 12 credits

  • MF728 Fixed Income Securities (core)
  • MF796 Computational Methods of Mathematical Finance (required elective)
  • FE829 Futures, Options, & Financial Risk Management (required elective)
  • Elective – Choose 1 from the following list:
    • MF840 Data Analysis and Empirical Methods (elective)
    • AC860 Accounting for Risk Management (elective)

Summer Semester

  • Optional internship

Fall Semester 2nd Year – 12 credits

  • MF731 Corporate Risk Management (required elective)
  • MF772 Credit Risk (required elective)
  • Electives – Choose 2 from the following list:
    • MF730 Portfolio Theory (elective)
    • MF770 Advanced Derivatives (elective)
    • MF850 Advanced Computational Methods (elective)


Analytics & Research

Fall Semester – 12 credits:

  • Core Curriculum*

* Students require at least a B+ average and a B+ in FE918 in order to pursue this track.

Spring Semester – 12 credits:

  • MF728 Fixed Income Securities (core)
  • FE920 Advanced Capital Markets (required elective – joint MF/Econ. PhD)
  • MF921 Advanced Topics in Asset Pricing (required elective – joint MF /Econ. PhD)
  • Elective – Choose 1 from the following list:
    • MF794 Stochastic Optimal Control and Investment (elective)
    • MF796 Computational Methods of Mathematical Finance (elective)

Summer Semester

  • Optional internship

Fall Semester 2nd Year – 12 credits:

  • MF730 Portfolio Theory (required elective)
  • MF770 Advanced Derivatives (required elective – joint with MSMF and Econ. PhD)
  • MF930 Advanced Corporate Finance (required elective – joint with MF, AC, Econ. PhD)
  • Elective – Choose 1 from the following list:
    • MF772 Credit Risk (elective)
    • MF850 Advanced Computational Methods (elective)


Prerequisites

Questrom School of Business requires that applicants have completed the following prerequisite courses to be considered for admission.  You will be asked to highlight your coursework within the online application.

Calculus I: Limits; derivatives; differentiation of algebraic functions. Applications to maxima, minima, and convexity of functions. The definite integral, the fundamental theorem of integral calculus, and applications of integration.

Calculus II: Logarithmic, exponential, and trigonometric functions; Sequences and series, and Taylors series with the remainder; Methods of integration.

Calculus III: Vectors, lines, and planes. Multiple integration, and cylindrical and spherical coordinates. Partial derivatives, directional derivatives, scalar and vector fields, the gradient, potentials, approximation, multivariate minimization, Stokes’s, and related theorems.

Linear Algebra: Matrix algebra, solution of linear systems, determinants, Gaussian elimination, fundamental theory, and row-echelon form. Vector spaces, bases, and norms. Computer methods. Eigenvalues and eigenvectors, and canonical decomposition. Applications.

Differential Equations: First-order linear and separable equations, Second-order equations and first-order systems, Linear equations and linearization, Numerical and qualitative analysis, Laplace transforms, Applications and modeling of real phenomena throughout.

Basic computer programming skills.

MF600 Math Refresher (0 credits. This course is optional)

The Mathematical Finance Program has a very strong quantitative component, one which many incoming students underestimate. Although students admitted to the program have satisfied the prerequisites in Mathematics, the program’s prerequisites represent the minimal, not the optimal, background required. Even if you have learned the topics required as prerequisites, reviewing these concepts immediately prior to the start of the program could be enormously helpful and will certainly increase your chance of success in the program. The course will begin with a review of matrix algebra, then proceed to examine the role of calculus in comparative static analysis.Following this, unconstrained and constrained optimization will be covered using multivariate calculus. The second half of the class deals with dynamics, beginning with a review of integration, and continuing with first- and higher-order differential equations.


Suggested Reading and Online Courses

The Mathematical Finance program is a multi-disciplinary program with its curriculum comprising from the fields of finance, applied mathematics, and computer science.  Before entering the program, it is suggested that students may read from the following books:

  1. Finance
    1. John Hull’s Options, Futures, and Other Derivatives. The so-called Bible of Wall Street Professionals, this book is mandatory reading for everyone entering the mathematical finance field.  Somewhat dry at times, but the topics covered, presentation, and relevance to the program has no equal.
    2. Saleh Neftci’s Principles of Financial Engineering. A great synopsis of the interaction between financial instruments and asset classes within the markets. The late Professor Neftci was truly a gifted writer.
  2. Applied Mathematics
    1. Steven Shreve’s Stochastic Calculus for Finance books: namely Stochastic Calculus for Finance I: The Binomial Asset Pricing Model and Stochastic Calculus for Finance II: Continuous-Time Models.  These books are standards for courses in stochastic calculus, but caution, these books can be hard to read the first time through especially the Continuous-Time Models.
    2. Neil Chriss’ Black Scholes and Beyond. An outdated book by some standards, but an easy to read account of fundamental stochastic calculus, probability, and statistics used in pricing options.
  3. Computer Science
    1. Paul Teetor’s R Cookbook. A great, simple to read and do tutorial on the R scripting language and R framework.  Many courses will rely on R or some statistical-based package.  Being proficient in R will be a great time saver as well as tool that will be useful for all time.
    2. Yuh-Dauh Lyuu’s Financial Engineering and Computation.  A great book that touches mainly on the computational aspects of mathematical finance.
    3. Any 3rd generation computer programming language book on C++.

There are some wonderful online-courses as well.

For mathematics, the following are suggested courses:

  1. Probability theory: https://www.coursera.org/course/probability
  2. Statistics and Inference: https://www.coursera.org/course/statistics
  3. Linear algebra: https://www.coursera.org/course/matrix
  4. Linear optimization: https://www.coursera.org/course/linearopt

For computer programming, the following are suggested courses:

  1. R Programming: https://www.coursera.org/course/rprog
  2. The Data Scientist’s Toolbox: https://www.coursera.org/course/datascitoolbox

And for those students that want to get a head start on mathematical finance:

  1. Mathematical Finance: https://www.coursera.org/course/mathematicalmethods
  2. Financial Engineering and Risk Management Part 1: https://www.coursera.org/learn/financial-engineering-1
  3. Financial Engineering and Risk Management Part 2: https://www.coursera.org/learn/financial-engineering-2