The needs of the modern finance, risk, and insurance industries demand a broad interdisciplinary and computationally oriented approach to educating the next generation of financial researchers, analysts, risk managers, and financial information technology professionals. The Computational Finance program addresses these needs by leveraging faculty expertise in a number of departments to integrate education and research across the following key areas: (a) finance concepts and theory; (b) mathematics, statistics and econometric modeling and analysis methods needed to model, analyze and predict the behavior of financial assets; and (c) computer science and information systems tools needed to implement modeling and analysis methods in finance industry organizations. The participating departments are: Economics, Finance, Mathematics, and Statistics.
Computational Finance and Financial Econometrics (ECON 424)
This course is an introduction to computational methods and statistical analysis in finance. It utilizes concepts from microeconomics, finance, mathematical optimization, data analysis, probability models, statistical analysis and econometrics. Topics in financial economics include asset return calculations, portfolio theory, index models, the capital asset pricing model and investment performance analysis. Computational topics covered include optimization methods involving equality and inequality constraints and basic matrix algebra. Statistical topics to be covered include probability and statistics with the use of calculus, descriptive statistics and data analysis, linear regression, basic time series methods, bootstrapping and the simulation of random data. The course will utilize Microsoft Excel, the S-PLUS statistical modeling language and the S+FinMetrics module.
Derivatives: Theory, Statistics and Computation (STAT 547)
European and American options, futures, forwards, exotic options. Ito process, Ito's lemma and Black-Scholes via risk neutral pricing. Binomial and trinomial tree models. Delta and gamma hedging. Implied volatility and volatility smile. Implied binomial trees. Management of market risk via value-at-risk and expected tail loss. Derivative pricing under deviations from assumptions of Black-Scholes: non-Gaussian returns, jump-diffusion models, time-varying volatility. Volatility estimation via EWMA and GARCH models. Yield curves and forward rates. Interest rate models, interest derivatives, introduction to credit derivatives. Computational methods and use of empirical price and returns data is an important component of the course. S-PLUS will be used for computational tasks such as exploring the distribution of asset returns, writing binomial tree pricing model methods, Monte Carlo pricing of exotic derivatives, estimating implied volatilities and volatilities, estimating the volatility smile, yield curve and forward rate smoothing, binomial and trinomial tree models for interest rate derivative pricing.
Doctoral Seminar in Capital Market Theory (FIN 590)
Decision making under uncertainty, information and capital market efficiency, portfolio theory, capital asset pricing model, arbitrage pricing model, and options pricing model.
Introduction to Financial Engineering (IND E 599B)
The techniques presented in the course emphasize a cash flow approach. Topics include deterministic cash flow analysis (time value of money, present value, internal rate of return, taxes, inflation), fixed income securities, duration and bond portfolio immunization, term structure of interest rates (spot rates, discount factors, forward rates), Fisher-Weill duration and immunization, capital budgeting, dynamic optimization problems, investments under uncertainty, mean-variance portfolio theory, capital asset pricing, forwards, futures, swaps, and hedging risk.
Statistical Computing III (STAT 538)
This course will cover various methods for solving optimization problems occuring in data fitting, such as the Choleski, SVD, and conjugate gradient methods for linear least squares, algorithms for penalized least squares with L2 and L1 penalty, gradient boosting, the Marquardt method for nonlinear least squares, Newton and quasi-Newton methods, and the EM algorithm for maximum likelihood estimation. The course also discusses motivating examples from a variety of areas.
Stochastic Calculus for Option Pricing (MATH/STAT 492)
This course presents the foundations of stochastic calculus needed for the Black-Scholes theory of option pricing. As prerequisites the students are assumed to know the basic notions of probability such as independence, expectation, and distribution, and similarly the basic notions of mathematical analysis, such as integration and elementary differential equations, along with analytical maturity. The material is presented without complete mathematical rigor in order to achieve breadth of coverage. However enough mathematical details, including selected proofs, are provided so that the students will have an adequate foundation to read the relevant literature in the financial mathematics field. Material includes Brownian motion, stochastic integration, and the fundamental theorems of stochastic analysis in relation to financial applications.
Empirical Asset Pricing (FIN 592)
Empirical research in finance with emphasis on methodology and scientific method. Empirical research in market efficiency, capital asset pricing model, options pricing model, and impact of firms' dividend and financing decisions on firm value.
Statistical Methods of Portfolios (STAT 549)
Portfolio optimization via constrained quadratic programming. Real-world optimization constraints such as long/short investing, sector constraints, diversification constraints, and transaction costs. Use of factor models for portfolio optimization and risk calculations. Active management, residual risk and return, information rules, forecasting, benchmark tracking, performance attribution, back-testing. Use of modern statistical methods: bootstrap re-sampling assessment of variability, robust methods for dealing with outliers, and non-Gaussian modeling of returns. Modern alternatives to mean-variance optimality: value-at-risk (VaR) and conditional value-at-risk (CVaR). Introduction to market risk and credit risk management. Portfolio optimization will be carried out using the S+NUOPT product that provides LP, QP, active set methods and interior point methods for solving large-scale portfolio optimization problems encountered in practice.
Simulation Methods in Finance (STAT 593)
Statistical foundations of Monte Carlo simulation in finance, with a focus on applications to pricing derivative products. Basic probability and statistics tools, pseudo-random number generators, low-discrepancy numbers, Monte Carlo accuracy, and variance reduction techniques. Simulating generalized Weiner processes and Ito processes. Models for multivariate asset price simulation, including copula models for cross-sectional correlation. Pricing exotic options via Monte Carlo. The BGM/J framework, Bermudan and European swaptions, exercise boundry calculations. Software implementation, testing and evaluation of selected methods for pricing some types of derivatives is an important ingredient of the course.
Management of Financial Risk (FIN 562)
Modern tools for managing financial risk. Fixed income securities and interest rate risk, credit risk, foreign currency risk, and insurance. Emphasis on use of futures, forwards, swaps, and option contracts.