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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.<\/p>\n
A distinctive aspect of the program is the Practitioners’ Seminar<\/a>, which brings leading industry specialists in quantitative finance directly into the classroom each semester.<\/p>\n For credit requirements, degree requirements, course sequencing, and academic policies, please see the Degree Requirements<\/a><\/span> page.<\/p>\n<\/div><\/div><\/div><\/div><\/div> 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<\/a><\/span> 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<\/a><\/span> page<\/p>\n<\/div> MATH 5010 GR Introduction to the Mathematics of Finance<\/span><\/p>\n 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.<\/p>\n<\/div>\n MATH 5030 GR Numerical Methods in Finance<\/span><\/p>\n 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.<\/p>\n<\/div>\n MATH 5050 GR Practitioners’ Seminar I (Fall Semester Only, 1.5 credits)<\/span><\/p>\n MATH 5051 GR Practitioners’ Seminar II (Spring Semester Only, 1.5 credits)<\/span><\/p>\n 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.<\/p>\n STAT 5263 GR Statistical Inference \/ Time-Series Modeling<\/span><\/p>\n 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.<\/p>\n<\/div>\n STAT 5264 GR Stochastic Processes \u2013 Applications I<\/span><\/p>\n 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.<\/p>\n<\/div>\n STAT 5265 GR Stochastic Methods in Finance<\/span><\/p>\n 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.<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div> 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.<\/p>\n<\/div>Mandatory Courses<\/b><\/h2>\n
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MAFN Elective Courses<\/b><\/h2>\n