MSMFT Academics & Curriculum

COURSE CODE: mf602

This course reviews computational problem-solving for mathematical finance in the Python programming language. The course covers the fundamentals of programming (functions, recursion, iteration), object-orientation, working with data files, numeric programing, simulation, and graphing. Finance-specific applications include: time value of money and bond pricing/analytics, descriptive statistics, matrix operations and linear algebra, pricing options, efficient (minimum variance) portfolios, event studies, and back-testing trading strategies.

COURSE CODE: MF610

This course prepares students in the MS Mathematical Finance program for the global employment market in quantitative finance. The course has the following objectives: to familiarize students with the foundational mathematics and statistics required for the MSMF program, to develop sound networking and job search strategies, to prepare students for ‘quant' interviews, to develop good career management habits, and to familiarize students with important developments in financial markets and issues of the day that affect the global financial services industry.

COURSE CODE: mf702

securities, forward and futures contracts, exchanges, market indexes, and margins); interest rates, present value, yields, term structure of interest rates, duration and immunization of bonds, risk preferences, asset valuation, Arrow-Debreu securities, complete and incomplete markets, pricing by arbitrage, the first and the second fundamental theorems of Finance, option pricing on event trees, risk and return (Sharpe ratios, the risk-premium puzzle), the Capital Asset Pricing Model, and Value-at-Risk.

COURSE CODE: mf790

This is a first course in stochastic calculus for finance, aiming to give students a comprehensive introduction to stochastic calculus. Concepts needed from probability theory and real analysis are reviewed. Results in stochastic calculus are illustrated via a large collection of examples. Intuition and applications are emphasized. Black-Scholes theory on pricing and hedging of derivatives and its associated tools from stochastic calculus are discussed in detail. The stochastic calculus content of the course is also used for fixed income, advanced derivatives, credit risk models, foreign exchanges, and commodities.

COURSE CODE: mf793

This course provides an introduction to R and Exploratory Data Analysis, Time Series Analysis, Multivariate Data Analysis, and Elements of Extreme Value Theory. This course also covers an array of statistical techniques used for simulation, parameter estimation, and forecasting in Finance.

COURSE CODE: mf610

This course prepares students in the MS Mathematical Finance program for the global employment market in quantitative finance. The course has the following objectives: to familiarize students with the foundational mathematics and statistics required for the MSMF program, to develop sound networking and job search strategies, to prepare students for ‘quant' interviews, to develop good career management habits, and to familiarize students with important developments in financial markets and issues of the day that affect the global financial services industry.

COURSE CODE: mf728

The course focuses on the valuation, hedging and management of fixed income securities. Fixed income instruments are by far the most important asset class in financial markets. Basic theoretical and empirical term structure concepts are introduced. Short rate models and the Heath-Jarrow-Morton methodology are presented. Market Models and their application for the valuation of forwards, swaps, caps, floors and swaptions, and other interest rate derivatives are discussed in detail.

COURSE CODE: mf796

This course develops algorithmic and numerical schemes that are used in practice for pricing and hedging financial derivative products. Focus is given on Monte-Carlo simulation methods (generation of random variables, exact simulation of stochastic processes, discretization schemes for pricing and hedging of contingent claims, variance reduction techniques, and estimation of sensitivities with respect to model parameters), model calibration to market data, and estimation of model parameters.

COURSE CODE: mf810

The course introduces students to a number of efficient algorithms and data structures for fundamental computational problems across a variety of areas within data science and blockchains. A special programming language for blockchain technology, such as Solidity, will be taught. Advanced techniques for improving computational performance, including the use of parallel computation and GPU acceleration are surveyed. Frameworks for big data analysis such as Apache Hadoop and Apache Spark are studied. Students will have the opportunity to employ these techniques and gain hands-on experience developing advanced applications.

COURSE CODE: mf815

This course surveys the application of machine learning techniques to data characterized by low signal-to-noise ratios and non-stationarity, properties of many financial datasets. Challenges associated with the application of “data-hungry” techniques such as deep learning to small-to-medium size datasets, often encountered in finance, are addressed.

COURSE CODE: mf821

In an increasing era of computerized trading, quantitative strategies are handling an ever greater share of market trading. This course details the use of quantitative methods in the development and implementation of trading strategies in the equity and debt markets with focus on both the market-making and proprietary trader perspectives. Both end-of-day and intraday strategies will be discussed with emphasis on the development, back testing methodology, and performance attribution of any strategy. Students will be grouped into market making and proprietary trading teams with the goal of generating positive P&L against each other.

COURSE CODE: mf825

This course is designed for students seeking to work as quants in a quantitative finance investments group. It covers utility theory, portfolio optimization, asset pricing, and some aspects of factor models, incorporating the impact of parameter uncertainty. The course does not cover risk management or fixed income instruments, nor does it describe how the financial services industry works. Rather, it teaches how a quant should optimize a portfolio. The course makes extensive use of R (Excel or VBA are not substitutes), optimization theory, statistics, regression theory (OLS, GLS, testing theory), and matrix algebra. Students should be very comfortable with these concepts before taking the course; further, students should already have taken a finance course covering expected returns models (CAPM), options and futures. The course emphasizes the ability to prove theoretical results and their validity, an essential trait for investments quants. Students who completed QST FE825 may not take this course for credit. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

COURSE CODE: mf840

This is the second course of the econometrics sequence in the Mathematical Finance program. The course quickly reviews OLS, GLS, the Maximum Likelihood principle (MLE). Then, the core of the course concentrates on Bayesian Inference, now an unavoidable mainstay of Financial Econometrics. After learning the principles of Bayesian Inference, we study their implementation for key models in finance, especially related to portfolio design and volatility forecasting. We also briefly discuss the Lasso and Ridge methods, and contrast them with the Bayesian approach Over the last twenty years, radical developments in simulation methods, such as Markov Chain Monte Carlo (MCMC) have extended the capabilities of Bayesian methods. Therefore, after studying direct Monte Carlo simulation methods, the course covers non-trivial methods of simulation such as Markov Chain Monte Carlo (MCMC), applying them to implement models such as stochastic volatility.

COURSE CODE: mf650

MF 650 is offered to MS and PhD candidates in Mathematical Finance. The course affords graduate students the opportunity to complete an internship in the financial services (or a related) industry and serves to enhance the students' academic and/or research experience. MF 650 is required for all students pursuing the MSMF degree. It is an elective for those pursuing the PHD in MF and has to be approved by the student's faculty advisor, department PhD Liaison and the PhD Program Director.

COURSE CODE: mf610

This course prepares students in the MS Mathematical Finance program for the global employment market in quantitative finance. The course has the following objectives: to familiarize students with the foundational mathematics and statistics required for the MSMF program, to develop sound networking and job search strategies, to prepare students for ‘quant' interviews, to develop good career management habits, and to familiarize students with important developments in financial markets and issues of the day that affect the global financial services industry.

COURSE CODE: MF730

A concise introduction to recent results on optimal dynamic consumption-investment problems is provided. Lectures will cover standard mean-variance theory, dynamic asset allocation, asset- liability management, and lifecycle finance. The main focus of this course is to present a financial engineering approach to dynamic asset allocation problems of institutional investors such as pension funds, mutual funds, hedge funds, and sovereign wealth funds. Numerical methods for implementation of asset allocation models will also be presented. The course also focuses on empirical features and practical implementation of dynamic portfolio problems.

COURSE CODE: mf731

This course provides an introduction to modern methods of risk management. Lectures cover risk metrics, measurement and estimation of extreme risks, management and control of risk exposures, and monitoring of risk positions. The impact of risk management tools, such as derivative securities, will be examined. Issues pertaining to the efficiency of communication architectures within the firm will be discussed. Regulatory constraints and their impact on risk management will be assessed. The approach to the topic is quantitative. The course is ideal for students with strong quantitative backgrounds who are seeking to understand issues pertaining to risk management and to master modern methods and techniques of risk control.

COURSE CODE: mf740

The course covers the following topics: introduction to blockchains and crypocurrencies; contract theory for initial coin offerings; robo-advising; crowd wisdom; and privacy issues. Although the course introduces some blockchain programming languages, e.g. Solidity, the emphasis of the course is on the economics of FinTech rather than on programming. The prerequisites include basic financial economics, econometrics, and stochastic processes.

COURSE CODE: mf770

This course provides a comprehensive and in-depth treatment of valuation methods for derivative securities. Extensive use is made of continuous time stochastic processes, stochastic calculus and martingale methods. The main topics to be addressed include (i) European option valuation, (ii) Exotic options, (iii) Multiasset options, (iv) Stochastic interest rate, (v) Stochastic volatility, (vi) American options and (vii) Numerical methods. Additional topics may be covered depending on time constraints.

COURSE CODE: mf772

This course covers asset pricing models (preferences, utility functions, risk aversion, basic consumption model, the mean-variance frontier, factor models, and robust preferences); and options pricing and risk management (arbitrage pricing in a complete market, delta-hedging, risk measure, and value-at-Risk).

COURSE CODE: mf850

This course explores algorithmic and numerical schemes used in practice for the pricing and hedging of financial derivative products. The focus of this course lies on data analysis. It covers such topics as: stochastic models with jumps, advanced simulation methods, optimization routines, and tree-based approaches. It also introduces machine learning concepts and methodologies, including cross validation, dimensionality reduction, random forests, neural networks, clustering, and support vector machines.

COURSE CODE: ac860

The objective of this course is to provide students who have no previous accounting knowledge with the accounting tools necessary for a better understanding of a firm's fundamentals, to enable a meaningful economic assessment of the firm's risk and potential return.