16:958:535 Advanced Statistical Methods in Finance (3) Useful concepts for statistical analysis of financial data: time value of money, theory of interest, discounted cash flow models, P/E multiples. Advanced distribution theory, statistical inference and hypothesis testing procedures, with applications in descriptive analysis of financial data (distribution, tail behavior, inference and testing various aspects of financial data) and detection of irrational and abnormal behaviors, such as herding and excessive risk taking. Advanced regression analysis with applications in pricing models (capital asset pricing model, multifactor pricing models and arbitrage pricing theory), credit rating, exchange rate modeling, and interest rate management. Multivariate analysis, principle components analysis, canonical correlation, and factor models, with applications in alternative-pricing models, risk factors, high frequency data, and market microstructure. Nonparametric methods (density estimation, nonparametric regression, and smoothing), with applications in technical analysis, term structure and yield curves, and risk-neutral density estimation. Robust variance-covariance estimation with applications in portfolio construction, diversification, optimization, and risk hedging. Decision theory (Bayesian and non-Bayesian) with applications in financial decision making and return-risk evaluation. Model selection, checking, validation, and robustness, with applications in back-testing of financial models, robustness concerns, and other validations and safety measures, with special consideration for computer trading algorithms. Prerequisite: 16:958:563.

16:958:536 Financial Risk Evaluation and Management (3) The concept of uncertainty and risk, measurement of risk, principle of return and risk trade-off, introduction to insurance, and various insurance instruments in business and finance. Classical and stochastic risk models, ruin theory, claims modeling and evaluations, risk premium pricing, and loss distributions. Value-at-risk framework and related statistical issues. Shortfall risk and related statistical issues. Extreme value theory and risk management. Statistical methods for pricing of futures and options, including diffusion models, ARCH/GARCH models, statistical tools for model estimations, hedging strategies, risk-neutral evaluation, arbitrage strategies, the Greeks, and risk premiums. Statistical methods for measuring, pricing, and management of interest rate and currency risk. Statistical methods for measuring, pricing, and management of credit risk. Introduction to monetary regulations for banks and financial institutions. Prerequisite: 16:958:565.

16:958:563 Regression Analysis in Finance (3) Review of basic statistical theory and matrix algebra; general regression models, implementing regression techniques with computer applications, residual analysis, selection of regression models, response surface methodology, nonlinear regression models, experimental design models, and analysis of covariance. Emphasis on the use of regression methods in finance and risk management. Prerequisite: Level IV statistics.

16:958:565 Financial Time Series Analysis (3) Model-based forecasting methods, autoregressive and moving average models, ARIMA, ARMAX, ARCH, state-space models, estimation, forecasting and model validation, missing data, irregularly spaced time series, parametric and nonparametric bootstrap methods for time series, multiresolution analysis of spatial and time series signals, and time-varying models and wavelets. Emphasis on financial applications of time series methods. Prerequisite: 16:958:563 or permission of instructor.

16:958:582 Methods and Theory of Probability with Financial Applications (3) Emphasis is on methods and problem solving. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, and sampling distributions. Prerequisite: One year of calculus. Degree credit given for only one of 16:960:580, 16:958:582, or 16:960:592.

16:958:583 Methods of Statistical Inference with Financial Applications (3) Theory of point and interval estimation and hypothesis testing. Topics include sufficiency, unbiasedness, and power functions. Emphasis is on application of theory and the development of statistical procedures. Prerequisite: 16:958:582. Degree credit not given for both 16:958:583 and 16:960:593.

16:958:587 Advanced Simulation Methods for Finance (3) Modern simulation methods and advanced statistical computing techniques for financial applications. Introduction to Monte-Carlo simulation methods, variance reduction technique, the bootstrap methods, Markov chain Monte Carlo methods, Sequential Monte Carlo method, hidden Markov models, Bayesian methods, etc. Expect to use C++ and R for programming and data analysis. Emphasis on examples and applications from finance and risk management. Prerequisites: 16:958:563, and 16:198:443 or equivalent C++ course or permission of instructor.

16:958:588 Financial Data Mining (3) Databases and data warehousing, exploratory data analysis and visualization, an overview of data mining algorithms, modeling for data mining, descriptive modeling, predictive modeling, pattern and rule discovery, text mining, Bayesian data mining, observational studies. Emphasis on the use of data mining techniques in finance and risk management. Prerequisites: 16:958:563, and 16:198:443 or equivalent C++ course or permission of instructor.