MS in Mathematical Finance Curriculum
All of our courses were specifically designed with the field of mathematical finance in mind. The 17-month MS program includes three semesters of coursework and a summer internship. The program is 48 credits.
|16 Credits||16 Credits||0 Credits||16 Credits|
C++ Programming for Mathematical Finance
|Optional Summer Internship
Stochastic Methods of Mathematical Finance I
Fixed Income Securities
Corporate Risk Management
Statistical Methods of Mathematical Finance
Stochastic Optimal Control and Investment
Stochastic Methods of Mathematical Finance II
Computational Methods of Mathematical Finance
In the Spring Semester, MF820 Quantitative Strategies and Algorithmic Trading (2 Credits) is offered and is not mandatory for graduation.
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 on the Math Finance Checklist
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:
- 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.
- 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.
- Applied Mathematics
- 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.
- 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.
- Computer Science
- 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.
- Yuh-Dauh Lyuu’s Financial Engineering and Computation. A great book that touches mainly on the computational aspects of mathematical finance.
- Any 3rd generation computer programming language book on C++.
There are some wonderful online-courses as well.
For mathematics, the following are suggested courses:
- Probability theory: https://www.coursera.org/course/probability
- Statistics and Inference: https://www.coursera.org/course/statistics
- Linear algebra: https://www.coursera.org/course/matrix
- Linear optimization: https://www.coursera.org/course/linearopt
For computer programming, the following are suggested courses:
- R Programming: https://www.coursera.org/course/rprog
- 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:
- Mathematical Finance: https://www.coursera.org/course/mathematicalmethods
- Financial Engineering and Risk Management Part 1: https://www.coursera.org/learn/financial-engineering-1
- Financial Engineering and Risk Management Part 2: https://www.coursera.org/learn/financial-engineering-2