### Cutting-edge curriculum

The three-semester program takes you to the cutting edge of financial engineering. The curriculum starts with tools such as stochastic calculus, derivatives, or computational methods necessary in most aspects of our fields. It then lets you explore your special interests, be it quantitative portfolio or risk management, fixed income or equity, You will be exposed to the latest techniques used in financial technology and statistical data analysis. You can explore exciting new frontiers such as machine learning and algorithmic trading.

A number of our students choose to supplement their degree with an optional fourth semester and obtain the Graduate Certificate in Advanced Financial Technology (GCAFT). As a standalone, the GCAFT is a four-course program exposing students to the latest advances in Fin. Tech., machine learning, statistical data science, cloud computing, blockchain, and cryptocurrencies. If you take it after your Questrom, MSMFT, you will likely already have taken some of these courses. Your requirement to get the GCAFT in addition to your MSc will be to complete 4 Fin. Tech. courses over your 4 semesters. You will have the freedom to choose appropriate courses in and outside of Questrom to complete your 4 courses, with the advice of the Executive Director.

An undergraduate degree in a quantitative discipline such as mathematical economics or finance, financial engineering, quantitative finance, statistics or econometrics, engineering, mathematics, physics, or computer science, is highly recommended for the program.

*The MS in Mathematical Finance & Financial Technology program at the Questrom School of Business is currently designated by US Department of Homeland Security (DHS) as a STEM-eligible degree program. International students in F-1 student status may be able to apply for a 24-month extension of their 12-month Optional Practical Training (OPT) employment authorization. More information about **STEM OPT eligibility** **is available from the BU International Students and Scholars Office (ISSO).*

## Curriculum

The MSMFT is a full-time, three-semester program. You take four courses per semester. The first semester courses are mandatory core courses. Then you choose from electives related to your industry preference and the skills you wish to emphasize. Information sessions and one on one advising whenever you wish help you choose. There are only two constraints. First, some courses constitute natural sequence where the first (taught in the 2^{nd} semester) is a prerequisite for the second (taught in the 3^{rd}). Second, you will need to take at least one course designated as in the area of financial technology. The latter is not really a constraint as the quasi totality of our students typically want to take more than two courses designated as financial technology. This free structure will let you develop advanced proficiency in fields such as:

- Algorithmic trading and high-frequency data
- Big data analysis and cloud computing
- Blockchain and cryptocurrencies
- Credit and corporate risk management
- Derivatives valuation
- Expertise in R, Python, C++, Julia
- Machine learning and financial applications
- Portfolio theory and asset management
- Risk management
- Statistics and Financial Econometrics

Unless mentioned otherwise, all courses are 3 credits and are taken for letter grade. MF610 is also 3 credits but one credit per semester. Students take MF610 every semester. The summer internship course MF650 is 1 credit and Pass / Fail.

#### Mathematical Finance Career Management (QSTMF610)

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.

#### FIRST SEMESTER CORE COURSES

#### Fundamentals of Finance (QSTMF702)

This course covers such topics as: financial markets (bonds, stocks, derivative securities, forward and futures contracts, exchanges, market indices, 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, risk premia), and the Capital Asset Pricing Model. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Programming for Mathematical Finance (QSTMF703)

In-depth discussion of object-oriented programming with Python and C++ for finance and data applications. Topics include built-in-types, control structure, classes, constructors, destructors, function overloading, operator functions, friend functions, inheritance, and polymorphism with dynamic binding. Case study looks at the finite differences solutions for the basic models of financial derivatives; as well as the design and development of modular, scalable, and maintainable software for modeling financial derivatives. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Statistics for Mathematical Finance (QSTMF793)

This course covers the fundamental principles of statistics and econometrics. It is mandatory for all tracks of the MSc. program. The course first reviews the needed concepts in probabilities, properties of random variables, the classic distributions encountered in Finance. Then, we cover the principles of random sampling, properties of estimators, e.g., the standard moment estimators (sample mean, variance, etc..). The next major topic is the regression analysis. We study the OLS and GLS principles, review their properties, in the standard case and when ideal assumptions are not correct. The course ends with a study of time series ARMA models and volatility models such as GARCH and Risk-Metrics. The course makes intensive use of the R package. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Stoch Calculus (QSTMF790)

Students with appropriate preparation interested in academic mathematical finance research can request to take FE918 in place of MF702.

#### Doctoral Seminar in Finance (QSTFE918)

This doctoral course, is designed to provide students with an introduction to financial economics. This lecture-based course will cover no arbitrage conditions, preferences and risk aversion, portfolio selection, the capital asset pricing model, asset pricing and dynamic asset pricing. In addition to lectures, this class will include readings and assignments. Open to MBA students with faculty member's permission. Must have strong quantitative background and several courses in finance or economics.

#### SECOND SEMESTER COURSES

#### Computational Methods of Mathematical Finance (QSTMF796)

This course introduces common algorithmic and numerical schemes that are used in practice for pricing and hedging financial derivative products. Among others, the course covers Monte-Carlo simulation methods (generation of random variables, exact simulation, discretization schemes), finite difference schemes to solve partial differential equations, numerical integration, and Fourier transforms. Special attention is given to the computational requirements of these different methods, and the trade-off between computational effort and accuracy. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### FinTech Programming (QSTMF810)

The course introduces students to a number of efficient algorithms and data structures for computational problems across a variety of areas within FinTech. In the first half of the course, a special programming language for blockchains, such as Solidity, is taught, and TensorFlow, a special Python library for deep learning models, is used to solve stochastic control problems in finance. In the second half of the course, 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. (This course is reserved for students enrolled in the Graduate Certificate in Financial Technology.)

#### Advanced Machine Learning Applications for Finance (QSTMF815)

This course surveys applications of machine learning techniques to various types of financial datasets. This course starts with financial data structure and features, then introduces deep learning and advanced supervised learning techniques. We will examine several machine learning applications in pricing, hedging, and portfolio management. Advanced methods for clustering and classification such as support vector machine and unsupervised learning will be introduced. Reinforcement learning and its connection with optimal control will be discussed. Text data will be introduced and analyzed using text mining techniques. Machine learning techniques will be applied to asset allocation. Strategy back-testing and strategy risk will also be discussed. (This course is reserved for students enrolled in the Graduate Certificate in Financial Technology.)

#### Portfolio Construction (QSTMF825)

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.)

#### Data Analysis and Financial Econometrics (QSTMF840)

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. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Advanced Capital Markets (QSTFE920)

This course provides a comprehensive and in-depth treatment of modern asset pricing theories. Extensive use is made of continuous time stochastic processes, stochastic calculus and optimal control. In particular, martingale methods are employed to address the following topics: (i) optimal consumption- portfolio policies and (ii) asset pricing in general equilibrium models. Advances involving non-separable preferences, incomplete information and agent diversity will be discussed.

#### Topics in Dynamic Asset Pricing (QSTMF921)

This course provides a comprehensive and in-depth treatment of modern asset pricing theories. Extensive use is made of continuous time stochastic processes, stochastic calculus and optimal control. Particular emphasis will be placed on (i) stochastic calculus with jumps; (ii) asset pricing models with jumps; (iii) the Hamilton-Jacobi-Bellman equation and stochastic control; (iv) numerical methods for stochastic control problems in finance. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

- MF825 requires MF840 to be taken concurrently
- FE920 or MF921 can be selected by appropriately prepared students interested in academic research, with the approval of the director and the professor.

#### THIRD (FALL) SEMESTER COURSES

#### Accounting Risk Management (QSTAC860)

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.

#### Dynamic Portfolio Theory (QSTMF730)

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 covers empirical features and practical implementation of dynamic portfolio problems. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Corporate Risk Management (QSTMF731)

This course is an introduction to modern methods of risk management. The first half of the course focuses on market risk. Here, lectures cover risk measures (such as Value at Risk and Expected Shortfall), with a focus on computation of such measures in a dynamic, multi-asset environment using real-world data. In particular, students will learn to compute, back-test, and account for risk measures when both monitoring and constructing portfolios. Additionally, lectures cover scenario analysis, stress testing, and the measurement of severe tail risk via extreme value theory. In the second half of the course, lectures cover alternate types of risk. These include operational, liquidity, model, and counter-party credit risk. In particular, students will derive formulas for the valuation adjustments due to counter-party default. 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. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Economics of FinTech (QSTMF740)

The course covers the following topics: introduction to Blockchains and cryptocurrencies; 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. Students are expected to be familiar with basic financial economics, econometrics, and stochastic processes.

#### Advanced Derivatives (QSTMF770)

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. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Credit Risk (QSTMF772)

The derivatives market has experienced tremendous growth during the past decade as credit risk has become a major factor fostering rapid financial innovation. This course will provide an in-depth approach to credit risk modelling for the specific purpose of pricing fixed income securities and credit-risk derivatives. The course will explore the nature of factors underlying credit risk and develop models incorporating default risk. Types and structures of credit-derivatives will be presented and discussed. Valuation formulas for popular credit-derivatives will be derived. Numerical methods, for applications involving credit derivative structures and default risks, will be presented. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Algorithmic and High-Frequency Trading (QSTMF821)

This course will introduce concepts of electronic markets, and statistical and optimal control techniques to model and trade in these markets. We will begin with a description of the basic elements of electronic markets, some of the features of the data, its empirical implications and simple microeconomic models. Next, we will study statistical tools to estimate and predict price and volatility of the high-frequency price. Then we will investigate algorithmic trading problems from the stochastic optimal control perspective, including the optimal execution problem and show how to modify the classical approaches to include order-flow information and the effect that dark pools have on trading. Trading pairs of assets that mean-revert is another important algorithmic strategy, and we will see how stochastic control methods can be utilized to inform agents how to optimally trade. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Deep Learning, Statistical Learning (QSTMF850)

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. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

## Faculty

Our faculty are top authorities in the subject areas they teach. They will help you develop a skill set to set you apart in the competitive quantitative finance and fintech job markets.

## Graduate Certificate in advanced financial technology

##### The Graduate Certificate in Advanced Financial Technology equips you with the skills to compete in the most exciting new area of finance—FinTech.

The program exposes you to the very latest developments in machine learning, artificial intelligence, distributed ledger (blockchain) technologies, cryptocurrencies, and crowd wisdom, all with the most recent applications to finance.

##### Program Details

The Graduate Certificate in Advanced Financial Technology (GCAFT) is a one-semester, full-time program offered over one or two semesters, Spring and Fall. Candidates must hold a minimum of a Master’s degree in a quantitative discipline such as Mathematics, Computer Science, Engineering, Statistics, Quantitative Finance, Economics, Operations Research, etc. Candidates must complete four courses to satisfy the program requirements.

A minimum of **three courses** must be selected from the following:

#### Economics of FinTech (QSTMF740)

The course covers the following topics: introduction to Blockchains and cryptocurrencies; 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. Students are expected to be familiar with basic financial economics, econometrics, and stochastic processes.

#### FinTech Programming (QSTMF810)

The course introduces students to a number of efficient algorithms and data structures for computational problems across a variety of areas within FinTech. In the first half of the course, a special programming language for blockchains, such as Solidity, is taught, and TensorFlow, a special Python library for deep learning models, is used to solve stochastic control problems in finance. In the second half of the course, 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. (This course is reserved for students enrolled in the Graduate Certificate in Financial Technology.)

#### Advanced Machine Learning Applications for Finance (QSTMF815)

This course surveys applications of machine learning techniques to various types of financial datasets. This course starts with financial data structure and features, then introduces deep learning and advanced supervised learning techniques. We will examine several machine learning applications in pricing, hedging, and portfolio management. Advanced methods for clustering and classification such as support vector machine and unsupervised learning will be introduced. Reinforcement learning and its connection with optimal control will be discussed. Text data will be introduced and analyzed using text mining techniques. Machine learning techniques will be applied to asset allocation. Strategy back-testing and strategy risk will also be discussed. (This course is reserved for students enrolled in the Graduate Certificate in Financial Technology.)

#### Algorithmic and High-Frequency Trading (QSTMF821)

This course will introduce concepts of electronic markets, and statistical and optimal control techniques to model and trade in these markets. We will begin with a description of the basic elements of electronic markets, some of the features of the data, its empirical implications and simple microeconomic models. Next, we will study statistical tools to estimate and predict price and volatility of the high-frequency price. Then we will investigate algorithmic trading problems from the stochastic optimal control perspective, including the optimal execution problem and show how to modify the classical approaches to include order-flow information and the effect that dark pools have on trading. Trading pairs of assets that mean-revert is another important algorithmic strategy, and we will see how stochastic control methods can be utilized to inform agents how to optimally trade. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Data Analysis and Financial Econometrics (QSTMF840)

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. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### Deep Learning, Statistical Learning (QSTMF850)

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. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

Candidates may select a maximum of one graduate-level BU course (subject to GCFT committee approval). Candidates must satisfy course-specific prerequisites for the approved course, or secure the approval of the instructor to register. Examples of appropriate courses include:

#### Data Science Tools and Applications (CASCS506)

Covers practical skills in working with data and introduces a wide range of techniques that are commonly used in the analysis of data, such as clustering, classification, regression, and network analysis. Emphasizes hands-on application of methods via programming. Effective Fall 2019, this course fulfills a single unit in each of the following BU Hub areas: Research and Information Literacy, Teamwork/Collaboration.

#### Principles of Machine Learning (CASCS542)

Introduction to modern machine learning concepts, techniques, and algorithms. Topics include regression, kernels, support vector machines, feature selection, boosting, clustering, hidden Markov models, and Bayesian networks. Programming assignments emphasize taking theory into practice, through applications on real-world data sets.

#### Big Data Analytics for Business (QSTIS843)

This programming-based analytics course will cover how to perform statistical analysis of large datasets that do not fit on a single computer. We will design a Hadoop cluster on Google Cloud Platform to analyze these datasets. Utilizing Spark, Hive, and other technologies, students will write scripts to process the data, generate reports and dashboards, and incorporate common business applications. Students will learn how to use these tools through Jupyter Notebooks and experience the power of combining live code, equations, visualizations, and narrative text. Employer interest in these skills is very high. Basic programming in python, and basic analytics are prerequisite.

#### Advanced Data Structures (ENGEC504)

Review of basic data structures and Java syntax. Data abstraction and object-oriented design in the context of high-level languages and databases. Design implementation from the perspective of data structure efficiency and distributed control. Tailoring priority queues, balanced search trees, and graph algorithms to real-world problems, such as network routing, database management, and transaction processing.

#### Cloud Computing (ENGEC528)

Fundamentals of cloud computing covering IaaS platforms, OpenStack, key Big Data platforms, and data center scale systems. Examines influential publications in cloud computing. Culminates in a group project supervised by a mentor from industry or academia. Same as CAS CS 528. Students may not receive credits for both.

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### Apply to the MSMFT

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