Math Finance

  • 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 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 I
    This course provides the necessary background for using the general tools of stochastic calculus in the domain of mathematical finance. The topics include: information structures and financial markets (sample spaces, event trees, ó-algebras, and partitions), random variables and random processes, expected values and conditional expected values, probability distributions and change of measure, convergence of random variables, martingales and convergence of martingales, and the Brownian motion process.
  • 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 795: Stochastic Methods of Mathematical Finance II
    This course focuses on developing the necessary tools from stochastic calculus to be applied in the mathematical theory of finance. Topics include: stochastic integration, equivalent changes of probability, fundamental theorems of finance, stochastic differential equations, pricing and hedging of contingent claims, short-rate models, introduction to American options, and changes of numeraire.
  • GSM MF 810: Professional Practice Seminar
    The purpose of the Professional Practice Seminars is to give students a better understanding of the financial markets and introduce them to the career development skills needed to be successful in their internship and job searches. The Financial Markets Module will introduce students to the inner-workings of the markets, the market stakeholders, the organization of the markets, and the market jargon. The Career Preparation Module will teach students necessary communication skills for successful interviewing to leverage internship and full time opportunities. It will also help them identify their role in the industry, teach them how to establish a target list of companies and contacts, and guide them through how to strategically position themselves and their unique value through their personal brand.