Our Curriculum
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Curriculum Overview
The MAFN curriculum is built on a rigorous core of mandatory courses in mathematical finance, stochastic processes, and numerical methods, complemented by a wide range of elective options that allow students to tailor their studies to their academic and professional interests. Electives span MAFN’s own advanced offerings as well as courses from across Columbia’s schools and departments, reflecting the program’s breadth and its connections across one of the world’s leading research universities.
A distinctive aspect of the program is the Practitioners’ Seminar, which brings leading industry specialists in quantitative finance directly into the classroom each semester.
For credit requirements, degree requirements, course sequencing, and academic policies, please see the Degree Requirements page.
Mandatory Courses
All students are required to complete a set of mandatory courses unless a course waiver has been granted. For waiver policies and procedures, please refer to the Degree Requirements page. Mandatory courses are generally offered in both the fall and spring semesters. However, several of them must be taken in the first semester due to prerequisite sequencing within the curriculum. For details, please refer to the Degree Requirements page
MATH 5010 GR Introduction to the Mathematics of Finance
Introduction to mathematical methods in pricing of options, futures and other derivative securities, risk management, portfolio management and investment strategies with an emphasis of both theoretical and practical aspects. Topics include: Arithmetic and Geometric Brownian ,motion processes, Black-Scholes partial differential equation, Black-Scholes option pricing formula, Ornstein-Uhlenbeck processes, volatility models, risk models, value-at-risk and conditional value-at-risk, portfolio construction and optimization methods.
MATH 5030 GR Numerical Methods in Finance
Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Review of the basic numerical methods for partial differential equations, variational inequalities and free-boundary problems. Numerical methods for solving stochastic differential equations; random number generation, Monte Carlo techniques for evaluating path-integrals, numerical techniques for the valuation of American, path-dependent and barrier options.
MATH 5050 GR Practitioners’ Seminar I (Fall Semester Only, 1.5 credits)
MATH 5051 GR Practitioners’ Seminar II (Spring Semester Only, 1.5 credits)
This seminar offers participants the opportunity to listen to practitioners discuss a range of important topics in the financial industry. Topics may include portfolio optimization, exotic derivatives, high frequency analysis of data and numerical methods. While most talks require knowledge of mathematical methods in finance, some talks are accessible to a more general audience.
- Students are required to complete one of the two courses, but are strongly encouraged to complete both.
- Withdrawing from one of the two seminars obliges the student to take an additional approved elective course.
- See Practitioners’ Seminar page for more information.
STAT 5263 GR Statistical Inference / Time-Series Modeling
Available to SSP, SMP Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering.
STAT 5264 GR Stochastic Processes – Applications I
Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito’s formula, stochastic calculus. Stochastic exponentials and Girsanov’s theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.
STAT 5265 GR Stochastic Methods in Finance
Prerequisites: STAT 5264 GR. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.
MAFN Elective Courses
The following elective courses are offered directly by the MAFN program. These courses are not mandatory; students may choose their electives from across the university, subject to the constraints of the MAFN degree requirements and the constraints imposed by the schools and departments offering the courses.
MATH 5220 GR Quantitative Methods in Investment Management
Prerequisites: Knowledge of statistics basics and programming skills in any programming language. Surveys the field of quantitative investment strategies from a buy side perspective, through the eyes of portfolio managers, analysts and investors. Financial modeling there often involves avoiding complexity in favor of simplicity and practical compromise. All necessary material scattered in finance, computer science and statistics is combined into a project-based curriculum, which give students hands-on experience to solve real world problems in portfolio management. Students will work with market and historical data to develop and test trading and risk management strategies. Programming projects are required to complete this course.
MATH 5280 GR Capital Markets and Investments
Risk/return tradeoff, diversification and their role in the modern portfolio theory, their consequences for asset allocation, portfilio optimization. Capitol Asset Pricing Model, Modern Portfolio Theory, Factor Models, Equities Valuation, definition and treatment of futures, options and fixed income securities will be covered.
MATH 5300 GR Hedge Funds Strategies and Risk
The hedge fund industry has continued to grow after the financial crisis, and hedge funds are increasingly important as an investable asset class for institutional investors as well as wealthy individuals. This course will cover hedge funds from the point of view of portfolio managers and investors. We will analyze a number of hedge fund trading strategies, including fixed income arbitrage, global macro, and various equities strategies, with a strong focus on quantitative strategies. We distinguish hedge fund managers from other asset managers, and discuss issues such as fees and incentives, liquidity, performance evaluation, and risk management. We also discuss career development in the hedge fund context.
MATH 5400 GR Non-Linear Option Pricing
Prerequisites: Familiarity with Brownian motion, Ito’s formula, stochastic differential equations, and Black-Scholes option pricing. Nonlinear Option Pricing is a major and popular theme of research today in quantitative finance, covering a wide variety of topics such as American option pricing, uncertain volatility, uncertain mortality, different rates for borrowing and lending, calibration of models to market smiles, credit valuation adjustment (CVA), transaction costs, illiquid markets, super-replication under delta and gamma constraints, etc. The objective of this course is twofold: (1) introduce some nonlinear aspects of quantitative finance, and (2) present and compare various numerical methods for solving high-dimensional nonlinear problems arising in option pricing.
MATH 5420 GR Modeling and Trading Derivatives
Required Prerequisite: Math GR5010 Intro to the Math of Finance (or equivalent). Recommended Prerequisite: Math GR5010 Intro to the Math of Finance or Stat GR5264 Stochastic Processes – Applications I. The objective of this course is to introduce students, from a practitioner’s perspective with formal derivations, to the advanced modeling, pricing and risk management techniques of vanilla and exotic options that are traded on derivatives desks, which goes beyond the classical option pricing courses focusing solely on the theory. It also presents the opportunity to design, implement and backtest vol trading strategies. The course is divided in four parts: Advanced Volatility Modeling; Vanilla and Exotic Options: Structuring, Pricing and Hedging; FX/Rates Components: Discounting, Forward Projection, Quanto and Compo Options; Designing and Backtesting Vol Trading Strategies in Python.
MATH 5431 GR Advanced Machine Learning for Finance
The application of Machine Learning (ML) algorithms in the Financial industry is now commonplace, but still nascent in its potential. This course prepares the next generation of researchers and practitioners for the coming revolution, providing an advanced “deep dive” into machine learning methods (both theory and application) that are deemed to be useful for financial applications, including trading and investment management.
MATH 5490 GR Algorithmic Trading with Market Simulator (1.5 credits)
The course will cover the fundamentals of Algorithmic Trading, the discipline that brings together computer software, and financial markets to open and close trades based on programmed code. The goal of the course is to help the students to get familiar with the different techniques and strategies used in algorithmic trading and to let them experiment with classical and new algorithms they will create. During the course, the students will use a Trading Market Simulator: The Rotman Market Simulator – a platform which allows students to transact financial securities with each other on a real time basis. Using the simulator, the students will familiarize themselves with specific decision tasks associated with financial securities, market dynamics, and investment or risk management strategies and get ready for the Rotman Competition.
MATH 5510 GR MAFN Fieldwork (1 to 3 credits)
Prerequisites: Complete two consecutive full-time terms and the instructors permission. See the MAFN website for details. This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.
MATH 5520 GR Career Development for Quantitative Finance (0 credits)
This course helps the students understand the job search process and develop the professional skills necessary for career advancement. The students will not only learn the best practices in all aspects of job-seeking but will also have a chance to practice their skills. Each class will be divided into two parts: a lecture and a workshop. In addition, the students will get support from Teaching Assistants who will be available to guide and prepare the students for technical interviews.
MATH 5521 GR Topics in Mathematical Finance (0 credits)
The purpose of this course is for MA in Mathematics of Finance students to gain knowledge and practical skills that are essential in the finance industry. The course will run as a series of lectures and discussions on various relevant topics, such as business communications and career talks that may feature guest speakers from the industry as well as the full-time faculty members. This will prepare the students for their job search, networking, and in their industry jobs in the future.This is 0 credit Pass/Fail and MAFN student only.
MATH 5260 GR Programming for Quantitative & Computational Finance
This course covers programming with applications to finance. The applications may include such topics as yield curve building and calibration, short rate models, Libor market models, Monte Carlo simulation, valuation of financial instruments such as options, swaptions and variance swaps, and risk measurement and management, among others. Students will learn about the underlying theory, learn coding techniques, and get hands-on experience in implementing financial models and systems.
MATH 5320 GR Financial Risk Management and Regulation
Prerequisites: student expected to be mathematically mature and familiar with probability and statistics, arbitrage pricing theory, and stochastic processes. The course will introduce the notions of financial risk management, review the structure of the markets and the contracts traded, introduce risk measures such as VaR, PFE and EE, overview regulation of financial markets, and study a number of risk management failures. After successfully completing the course, the student will understand the basics of computing parametric VaR, historical VaR, Monte Carlo VaR, cedit exposures and CVA and the issues and computations associated with managing market risk and credit risk. The student will be familiar with the different categories of financial risk, current regulatory practices, and the events of financial crises, especially the most recent one.
MATH 5340 GR Fixed Income Portfolio Management
Prerequisites: comfortable with algebra, calculus, probability, statistics, and stochastic calculus. The course covers the fundamentals of fixed income portfolio management. Its goal is to help the students develop concepts and tools for valuation and hedging of fixed income securities within a fixed set of parameters. There will be an emphasis on understanding how an investment professional manages a portfolio given a budget and a set of limits.
MATH 5360 GR Math Methods in Financial Price Analysis
Course covers modern statistical and physical methods of analysis and prediction of financial price data. Methods from statistics, physics and econometrics will be presented with the goal to create and analyze different quantitative investment models.
MATH 5380 GR Multi-Asset Portfolio Management
The course will cover practical issues such as: how to select an investment universe and instruments, derive long term risk/return forecasts, create tactical models, construct and implement an efficient portfolio,to take into account constraints and transaction costs, measure and manage portfolio risk, and analyze the performance of the total portfolio.
MATH 5430 GR Machine Learning for Finance
The application of Machine Learning (ML) algorithms in the Financial industry is now commonplace, but still nascent in its potential. This course provides an overview of ML applications for finance use cases including trading, investment management, and consumer banking. Students will learn how to work with financial data and how to apply ML algorithms using the data. In addition to providing an overview of the most commonly used ML models, we will detail the regression, KNN, NLP, and time series deep learning ML models using desktop and cloud technologies. The course is taught in Python using Numpy, Pandas, scikit-learn and other libraries. Basic programming knowledge in any language is required.
MATH 5450 GR Credit Analytics
This course uses a combination of lectures and case studies to introduce students to the modern credit analytics. The objective for the course is to cover major analytic concepts, ideas with a focus on the underlying mathematics used in both credit risk management and credit valuation. We will start from an empirical analysis of default probabilities (or PD), recovery rates and rating transitions. Then we will introduce the essential concepts of survival analysis as a scientific way to study default. For credit portfolio we will study and compare different approaches such as CreditPortfolio View, CreditRisk+ as well as copula function approach. For valuation we will cover both single name and portfolio models.
MATH 5470 GR A Mathematical Approach to Generative AI
Generative AI (“GenAI”) is reshaping the global economy and the future of work by revolutionizing problem-solving, optimizing complex systems, and enabling data-driven decision-making. Its profound impact spans across natural language understanding, image generation, and predictive analytics, marking a paradigm shift that necessitates a deep and rigorous understanding of its mathematical foundations. This course is designed to equip students with a comprehensive framework for exploring the mathematical principles underpinning GenAI. Emphasizing statistical modeling, optimization, and computational techniques, the curriculum provides the essential tools to develop and analyze cutting-edge generative models.
MATH 5510 GR MAFN Fieldwork (1 to 3 credits)
Prerequisites: Complete two consecutive full-time terms and the instructors permission. See the MAFN website for details. This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.
Other Approved Electives
MAFN students have broad access to courses across Columbia University. While each elective requires case‑by‑case approval, the program typically evaluates requests using the following criteria:
1. The course must be graduate‑level and offered in person.
2. The course must be relevant to mathematical finance.
3. The course content should not significantly overlap with the required MAFN curriculum or with courses the student has already completed.
The following is a selection of courses from other departments and schools that MAFN students have taken and that have been approved as electives toward the degree.