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GSM MF 600: Math Refresher
The Mathematical Finance Program has a very strong quantitative component, one which many incoming students underestimate. Although students admitted to the program have satisfied the prerequisites in Mathematics, the program's prerequisites represent the minimal, not the optimal, background required. Even if you have learned the topics required as prerequisites, reviewing these concepts immediately prior to the start of the program could be enormously helpful and will certainly increase your chance of success in the program. The course will begin with a review of matrix algebra, then proceed to examine the role of calculus in comparative static analysis. Following this, unconstrained and constrained optimization will be covered using multivariate calculus. The second half of the class deals with dynamics, beginning with a review of integration, and continuing with first- and higher-order differential equations.
GSM MF 601: Preparation Week
Mathematical Finance Preparation Week is a combination of orientation activities, academic sessions, and career preparation designed to give you a foundational knowledge for the Mathematical Finance program. The week will include training on various tools you will need for the program, professional development sessions, and social gatherings.
GSM MF 702: Fundamentals of Finance
This course covers such topics as: financial markets (bonds, stocks, derivative 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.
GSM MF 703: C++ Programing for Mathematical Finance
In-depth discussion of object-oriented programming with C++ for mathematical finance. 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.
GSM MF 728: Fixed Income Securities
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.
GSM MF 730: Portfolio Theory
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.
GSM MF 731: Corporate Risk Management
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.
GSM MF 770: Advanced Derivatives
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.
GSM MF 772: Credit Risk
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).
GSM MF 792: Stochastic Methods of Mathematical Finance 1
This course provides the necessary background from measure-theoretic probability theory, which is essential for developing the methods of continuous-time finance, based on stochastic analysis. Main topics: measure spaces and probability structures, integration, information structures (sample spaces, event trees, sigma- algebras, and partitions), random variables, conditioning and independence, probability distributions and change of measure, convergence of random variables, random sampling, the binomial model and the connection between equilibrium asset pricing and martingales in discrete time.
GSM MF 793: Statistical Methods of Mathematical Finance
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.
GSM MF 794: Stochastic Optimal Control and Investment
Main topics: LÃ©vy processes and jump diffusion models in finance, classical problems for optimal control (Merton's problem, etc.), the Hamilton-Jacobi-Bellman equation, the connection between asset pricing and free-boundary problems for PDEs, optimal exercise of American-style derivatives, optimal investment decisions, valuation of real options, policy intervention, and applications to some macroeconomic models.
GSM MF 795: Stochastic Methods of Mathematical Finance 2
This course develops the basic tools from stochastic calculus needed for the study of continuous time finance. It also covers the basic principles and ideas of continuous time finance. Topics include: Brownian motion, continuous time martingales and semimartingales, stochastic integration, Girsanov's theorem, stochastic differential equations, contingent claims and hedging, the fundamental theorems of asset pricing.
GSM MF 796: Computational Methods of Mathematical Finance
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.
GSM MF 820: Quantitative Strategies and Algorithmic Trading
Graduate Prerequisites: GSM MF702; GSM MF769; GSM MF795.
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.
GSM MF 921: Topics in Dynamic Asset Pricing
This course provides a selective survey of the methods and results of classic papers and recent advances in the asset pricing literature. Extensive use is made of continuous time techniques. Topics will include state dependent preferences, long run and business cycle risks, money, term structure models, transaction costs, and intermediation.
GSM MF 930: Adv Crp Finance
GSM MF 999: Ds:Math Finance