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, the Black-Litterman Model, and Value-at-Risk.
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: finite differences solutions for the basic models of financial derivatives; design and development of modular, scalable, and maintainable software for modeling financial derivatives. Laboratory course.
The course provides an introduction to the valuation of fixed income securities, the management and hedging of fixed income portfolios and the valuation and usage of fixed income derivatives. Some of the contracts analyzed in the course include pure discount bonds, coupon bonds, callable bonds, floating rate notes, interest rate swaps, caps, floors, swaptions, inflation-indexed bonds, and convertible bonds. The course covers topics such as basic theoretical and empirical term structure concepts, short rate modeling, the Heath-Jarrow-Morton methodology and market models.
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 life cycle 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.
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.
MF770: 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.
MF772: 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).
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, σ-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.
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.
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.
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.
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.
Empirical literature in asset pricing, Implementation of MPT using financial econometric techniques. Empirical evidence on major Asset Pricing models (CAPM, APT, Factor Models – Fama-French-Carhart). Evidence on active management performance. Properties of performance evaluation criteria: Sharpe ratio, Jensen alpha, Information ratio, Henrikson-Merton. Optimal portfolio design. Covariance matrix modeling: factor-models (Factors & PCA), GARCH. Review & implement latest literature on optimal portfolio construction.
Quantitative methods for development & implementation of strategies for market-making & proprietary trading. End-of-day & intraday strategies, microstructure, hardware & software development issues, strategy back-testing & performance. Students grouped in market making & proprietary trading teams with goal of generating positive P&L against one another.
Review of Maximum Likelihood. In-depth coverage of Bayesian Econometrics. Prior & posterior distributions, prediction, model comparison by posterior odds ratios, model & optimal forecast combination. Markov Chain Monte Carlo (MCMC) simulation to implement time series models. Gibbs Sampling & Metropolis algorithms to simulate from posterior & predictive densities of future returns. Stochastic volatility & realized volatility modeling.
Expectations of multidimensional SP with jumps. Tools for asset pricing, portfolio & risk management. Minimization of computational costs. Numerical methods for PDEs: adaptive quadrature, finite element. Probabilistic methods: thinning & time changes of point processes, localization of diffusions, MCMC simulation, exact simulation. Filtering: Kalman & particle filters.
MF921: Topics in Dynamic Asset Pricing
Selective survey of methods & results of classic papers & recent advances in the asset pricing literature. Continuous time based. Topics: state dependent preferences, long run & business cycle risks, money, term structure models, transaction costs, intermediation.
MF930: Advanced Corporate Finance
Fundamental concepts: MM propositions. Agency cost theory. Asymmetric information. Bankruptcy. Initial public offerings. Dividends. Financial intermediation. Corporate governance. Financial contracting. Dynamic capital structure. Incentive contracts. Dynamic contracts.
FE825: Advanced Portfolio Theory
Reviews modern portfolio theory as approached in quantitative money management. Modern portfolio framework, implementation & problems, estimation of means, variances & co-variances, performance. Discussion of articles in Journal of Portfolio Management & Financial Analysts Journal.
FE829: Derivatives and Risk Management
Forward, futures, swaps, options. Hedging stocks, currencies, commodities. Models: binomial, Black-Scholes-Merton (BSM), extensions of BSM. Volatility: implied (VIX), actual. VaR.
FE918: Introduction to Financial Economics
Preferences & risk aversion. Stochastic dominance. Mathematics of efficient frontier. Portfolio separation. Equilibrium valuation of contingent claims. Optimal allocation of risks. Valuation. Differential information. Multi-period markets: equilibrium, no-arbitrage.
FE920: Advanced Financial Economics: Continuous Time and Asset Pricing
Consumption-portfolio choice: standard model, optimal portfolio, non-separable preferences, incomplete information. Asset pricing: separable preferences, non-separable preferences, heterogeneity, information & beliefs, market frictions.