Columbia University - MA in Mathematics of Finance

It has been a long time since the last review for this program, so I hope to provide some up-to-date information. Feel free to message me if you have any questions and I’ll try to get back to you. Just refrain from asking me to evaluate your profile, for files from any classes, or for more information on my background.


Things to note:
- Now that there is the 3rd semester option, it is no longer mandatory to take at least 5 courses per semester, thought 4 are required to have full-time status
- The MAFN program offers its own electives in the spring semester
- Career services have improved since the last reviews were posted and the program continues to build up its own individualized career services


Background
Engineering undergrad and IT work.


Did you get admitted to other programs?
Yes


Why did you choose this program (over others, if applicable)?
NYC location, university reputation, foundation in mathematics, flexibility in course selection


What alternative sources of info you used to learn more about the program?
QuantNet, Columbia MAFN website


Tell us about the application process at this program
Very straight-forward process outlined on the school website. Typically find out if you’re admitted around late May.


Tell us about the required courses in this program.
Fall semester:
MATH GR 5010 – Introduction to the Mathematics of Finance
A thorough, straight-forward overview of various product types and how they are priced, arbitrage, implementation of continuous-time stochastic processes, basic risk management, and basic portfolio construction. Taught by Professor Mikhail Smirnov, sample code/coding for homework is done in MatLab, but what programming language you use for the final project is up to you.

STAT GR 5263 – Statistical Inference/Time-Series Modelling
Course on modelling and inference for random processes. Has a good balance of theory and practical application. Professors vary by semester, but the course content is pretty much the same regardless of the professor you have. Most practical materials, as well as some exam and homework questions, were in R.

STAT GR 5264 – Stochastic Processes - Applications I
Course focused on the foundations of stochastic calculus and continuous-time stochastic processes. This class was the one that seemed to vary the most depending on which professor you had. I had Professor Lars Tyge Nielsen, who provided and taught from his own textbook chapters. His section seemed to focus more on the theory than the other section based on conversations I’ve had, but I found it to be a very thorough and interesting class.

Spring semester:
MATH GR 5030 - Numerical Methods in Finance
This course is still the same as it was when the last review for the program went up. It focuses on interpolation, root solving, finite differences, and some simulation depending on if there is enough time left in the semester. It goes into both the theory of the different techniques presented and the implementation of the techniques in Excel using VBA. Professor Tat Sang Fung is still the professor and is still a practitioner.

STAT GR 5265 – Stochastic Methods in Finance
This course focused mainly on the practical implementation of stochastic methods within finance, along with some mathematical and probabilistic tools for analyzing option markets. This includes pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, and term structure of interest rates. Can be some overlap with STAT GR 5264 in the beginning.

MATH GR 5050 – Mathematical Finance Practitioners Seminar
A seminar series inviting practitioners in the field of quantitative finance and some senior professors from other universities to discuss the work they do. As a result, the content varies from year to year, but it is still a great opportunity to hear from and speak to those in the industry.


Any elective courses in this program you like?
I liked all of the electives I took, but a few that stood out were:

MATH GR 5220 – Quantitative Methods in Investment Management
The whole class centers around a group project where you need to implement a trading strategy that includes accurate, unadjusted point-in-time data, forecasting, portfolio allocation, transaction costs, risk management, and performance analysis/reporting. Beyond this, the project is open-ended in terms of what sectors/products you want to focus on, programming language you want to use, etc. Professor Alexander Greyserman thoroughly explains what he is expecting and common pitfalls in the first few weeks, then proceeds to invite guest speakers consisting mostly of current financial practitioners who provide insight into how the aspects of the project are handled in practice.

IEOR E4732 – Computational Methods in Finance
Professor Ali Hirsa presents applications of a wide variety of computational techniques that are commonly utilized in quantitative finance, including transform (FFT, FrFT for de-noising and pricing), finite difference methods (for PDEs and PIDEs), Monte Carlo simulation, calibration, filtering, and parameter estimation techniques. Final project revolves around taking an existing code for a technique covered in the course and expanding upon it in a meaningful way. Lecture material and the final code are given in Python. I’d recommend taking this course after the Numerical Methods in Finance course, since it contains topics in that course, expands upon them, and adds more methods.

MATH GR 5360 – Mathematical Methods in Financial Analysis
Primarily focused on econophysics, this course provided by Alexei Chekhlov relates current statistical methods used in quantitative finance to different concepts seen in the worlds of engineering and physics. These include position sizing, statistical fluid mechanics/turbulence, Brownian/Random walks, variance ratio tests, memory effects, mean reverting vs push-response functions, and Levy distributions. Final project consists of developing and testing a trading strategy using concepts presented in the course.


Tell us about the quality of teaching
I found the teaching in my MAFN courses to be fantastic, with all of them having a firm grasp of the material, practical knowledge to offer, and willingness to help students outside the classroom if asked. There are also TAs for all classes, all of whom I’ve found to be incredibly helpful and often go out of their way to assist you understand material if you are willing to reach out to them.


Materials used in the program
For most classes, the professor will provide lecture notes/slides. Beyond this, the only outside materials from the required courses are:
MATH GR 5010: Options, Futures, and Other Derivatives by John C. Hull
STAT GR 5264 & 5265: Stochastic Calculus for Finance I and II by Steven Shreve


Projects
Most projects involve creating and back-testing trading strategies, with various degrees of complexity depending on the course. The only project from the required courses is the final project in MATH GR 5010, which is a straightforward creation of a trading strategy with some ties to topics covered within the course.

The practical portions of the MATH GR 5030 homework could also feel like projects, where you are to implement the numerical method you are currently learning that week within Excel/VBA.


Career Services
I see the Columbia Career Services get criticized a lot on here, to the point that many say they are no help at all. I have to respectfully disagree in this regard, as I have been able to take advantage of many great programs like resume help, mock interviews, career fairs, networking/social events, and Lionshare (job website) offered by the University-wide Career Services Center. There are also clubs like the Columbia Quant Group which hold networking and information sessions specifically for quantitative professionals/students.

From the MAFN program, I have been able to participate in employer information sessions and employer open houses aimed specifically towards MAFN students. The MAFN program has also recently hired a full-time career services counselor who provides a listing of job openings, outside employer events like information sessions and hackathons, and holds networking sessions between current students and alumni of the program.

Ultimately, career services and the MAFN program provide plenty of opportunities for you to get your name out there and put your best foot forward in the job hunt.


What do you like about the program?
- Its focus on mathematics and statistics.
- Flexibility in choosing which courses to take.
- Opportunities to meet with companies at info sessions/networking events and to hear from some of the most respected names in the industry through seminars.
- The many resources and opportunities available at Columbia University to explore things outside of your major requirements/courses (ie. I was able to participate in research).
- Projects within classes that have clear practical purposes and allow for flexibility in approach.


What DON’T you like about the program?
- Courses from the statistics department heavily favor R programming over other languages
- Though the number of electives offered in-house by the MAFN program has improved, it still has its limitations.
- The process to register for courses from the Business and Engineering School is not the easiest to find and you are limited to only one course from each in any given semester. You basically have to fill out a Google form for each school where you list 3 courses you’d like to take and hope your #1 choice has an open spot after the 2 weeks of registration are up.


Final Thoughts
I greatly appreciated the time I spent as a student in the Columbia MAFN program and hope that this write up offers some up-to-date new insight into the program. Another post I found helpful and which I think should be posted as a review can be found here:
https://quantnet.com/threads/some-information-about-columbia-mafn.20585/