### First Semester (Fall) | 13 Credits

##### REQUIRED COURSES

#### 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.

#### 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.

#### Programing 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.)

#### Stochastic Methods in Asset Pricing I (QSTMF795)

This course develops the basic tools from measure-theoretic probability theory and stochastic calculus that are needed for an in-depth study of continuous time finance. Some related tools from asset pricing (e.g., risk-preferences and state-price densities) are introduced as well, and the basic ingredients of continuous time financial modeling are developed. The following topics are covered: probability and measure, the coin-toss space and the random walk, random variables and convergence, Gaussian distribution, martingales, Brownian motion, stochastic integration for semi-martingales and Ito formula, Girsanov's theorem, stochastic differential equations, continuous time market models and pricing by arbitrage, resume of Malliavin calculus, replication and pricing of contingent claims, market completeness and the fundamental theorems of asset pricing. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

*To pursue this concentration, students must earn at least a B+ average and a B+ in QSTFE918*

### Second Semester (Spring) | 13 Credits

##### REQUIRED COURSES

#### 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.

#### Fixed Income Securities (QSTMF728)

The course focuses on the valuation, hedging and management of fixed income securities. 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. (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.)

*QSTFE920 and QSTMF921 are jointly offered to PhD students in Mathematical Finance and Economics*

##### ELECTIVES COURSES

Choose **one** of the following courses:

#### Stochastic Methods in Asset Pricing II (QSTMF794)

The course covers: the Feynman-Kac formula and the Fokker-Plank equation, stochastic calculus with jumps, Levy processes and jump diffusion models in finance, Bellman's principle of dynamic programming and the Hamilton-Jacobi- Bellman equation, classical problems for optimal control in finance (Merton's problem, etc.), investment-consumption decisions with transaction costs, the connection between asset pricing and free-boundary problems for PDEs, optimal stopping problems and the exercise of American-style derivatives, capital structure and valuation of real options and corporate debt, exchange options, stochastic volatility models, and Dupire's formula. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)

#### 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.)

### Third Semester (Fall) | 13 Credits

##### REQUIRED COURSES

#### 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.

#### 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.)

#### 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.)

#### Advanced Mathematical Finance (QSTMF922)

This course provides a rigorous introduction to the modern theory of mathematical finance in incomplete markets. The first part of the course covers the fundamental theorem of asset pricing, as well as super-hedging of contingent claims, in full generality for discrete time models. The second half of the class focuses on optimal investment, pricing and hedging in continuous time incomplete markets. Here, lectures will cover optimal investment and duality for general semi-martingale models; and portfolio optimization and pricing in Markovian factor models, non-Markovian Brownian models, models with trading constraints, and models with transactions costs. Throughout this half, lectures will highlight connections to the dynamic programming principle, the Martingale optimality principle, semi-linear Cauchy partial differential equations, backward stochastic differential equations, and the theory of viscosity solutions.

*QSTMF922 is jointly offered to PhD students in Mathematical Finance and Economics*

##### ELECTIVES COURSES

Choose **one** of the following courses:

#### 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.)

#### Advanced Computational Methods (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.)