Math Finance

• 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 728: Fixed Income Securities
  Term structure models are the basis for the valuation of any financial assets. Fixed income instruments are by far the most important asset class in today?s financial markets. The course focuses on the valuation, hedging, and management of fixed income securities. Basic theoretical and empirical term structure concepts are introduced. Basic short rate models are presented. The Heath-Jarrow-Morton term structure methodology is discussed in detail. Consistency requirements for the construction of term structure curves are presented. The Market LIBOR model and its application for the valuation of futures, forwards, swaps, caps, floors and swaptions, and other interest rate derivatives will be introduced. The course emphasizes both theoretical and practical aspects of term structure models and fixed income securities.
• 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: Advd Derivative
  
• 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 794: Stochastic Optimal Control and Investment
  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, Pontryagin?s principle of maximum, and applications to some macroeconomic models.
• 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 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
  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, intermediation.

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