Engineering Probability and Statistics II (ORIE 5500):
A rigorous foundation in theory combined with the methods for modeling, analyzing, and controlling randomness in engineering problems. Probabilistic ideas are used to construct models for engineering problems, and statistical methods are used to test and estimate parameters for these models. Specific topics include random variables, probability distributions, density functions, expectation and variance, multidimensional random variables, and important distributions including normal, Poisson, exponential, hypothesis testing, confidence intervals, and point estimation using maximum likelihood and the method of moments.
Prerequisite: ENGRD 2700 or equivalent.
Operations Research II: Introductory Engineering Stochastic Processes I (ORIE 3510)
Students use basic concepts and techniques of random processes to construct models for a variety of problems of practical interest. Topics include the Poission process, Markov chains, renewal theory, models for queuing, and reliability.
Computers and Programming (CS 2110/ENGRD 2110)
Intermediate programming in a high-level language and introduction to computer science. Topics include program structure and organization, object-oriented programming (classes, objects, types, sub-typing), graphical user interfaces, algorithm analysis (asymptotic complexity, big “O” notation), recursion, data structures (lists, trees, stacks, queues, heaps, search trees, hash tables, graphs), simple graph algorithms. Java is the principal programming language.
Prerequisite: CS 1110 or equivalent course in Java or C++.
Introduction to Derivatives, Part I (NBA 6730)
This course introduces students to the pricing and hedging of derivative securities. Briefly covers forward contracts, futures contracts, and swaps. The primary emphasis is on option contracts. Underlying assets include stocks, currencies, and commodities.
Introduction to Derivatives, Part 2 (NBA 6740)
This course's material is the second half of NBA 5460. The course introduces students to the pricing and hedging of derivative securities. The course briefly covers forward contracts, futures contracts and swaps. The primary emphasis is on option contracts. Underlying assets include stocks, currencies, and commodities. Fixed income derivatives are covered in NBA 5550. Class participation, assignments and a final exam determine the class grade. Together, NBA 6730 and NBA 6740 are equivalent to NBA 5460.
Prerequisite: NCC 5560 (Finance Core) or permission of the instructor. (Prescribed self-study can be substituted for this prerequisite.)
Financial Engineering with Stochastic Calculus I (ORIE 5600)
Introduction to continuous-time models of financial engineering and the mathematical tools required to use them, starting with the Black-Scholes model. Driven by the problem of derivative security pricing and hedging in this model, the course develops a practical knowledge of stochastic calculus from an elementary standpoint, covering topics including Brownian motion, martingales, the Ito formula, the Feynman-Kac formula, and Girsanov transformations.
Prerequisite: knowledge of probability at level of ORIE 3500/5500.
Optimization I (ORIE 5300)
Formulation of linear programming problems and solutions by the simplex method. Related topics such as sensitivity analysis, duality, and network programming. Applications include such models as resource allocation and production planning. Introduction to interior-point methods for linear programming.
Prerequisite: MATH 2210 or 2940.
Monte Carlo Simulation (ORIE 5581)
Introduction to Monte Carlo and discrete-event simulation. Emphasizes tools and techniques needed in practice. Random variate generation, input and output analysis, modeling using a discrete-event simulation package.
Prerequisite: OR&IE 3500/5500 (may be taken concurrently) and computing experience, or permission of instructor.
Monte Carlo Methods in Financial Engineering (ORIE 5582)
An overview of Monte Carlo methods as they apply in financial engineering. Generating sample paths. Variance reduction (including quasi random number), discretization, and sensitivities. Applications to derivative pricing and risk management.
Applied Financial Engineering (ORIE 5961)
This course has two components: a sequence of lectures and a project. The lectures are given by the faculty for the course and by invited speakers from the financial industry. Project satisfies M.Eng. project requirement.
Prerequisite: M.Eng. F.E. students only.
Financial Engineering with Stochastic Calculus II (ORIE5610)
Building on the foundation established in ORIE 5600, this course presents no-arbitrage theories of complete markets, including models for equities, foreign exchange, and fixed-income securities, in relation to the main problems of financial engineering: pricing and hedging of derivative securities, portfolio optimization, and risk management. Other topics include model calibration and incomplete markets.
Prerequisite: ORIE 5600.
Topics in Linear Optimization (ORIE 5311)
Extension of ORIE 5300 that deals with applications and methodologies of dynamic programming, integer programming, and large-scale linear programming.
Pre- or corequisite: M.Eng. students in ORIE; ORIE 5300. Not open to students who have already taken ORIE 3310 or 5310.
Statistics for Financial Engineering (ORIE 5640)
Investments and Portfolio Analysis (NBA 5420)
This course emphasizes both conceptual foundations and practical implementation. The material in the course would be helpful to anyone interested in investing. However, the course should be especially useful to students interested in an investment management career (e.g., portfolio management in mutual funds and hedge funds, equity research, equity trading, risk management, investment consulting, and investment banking). After a brief review of fundamental issues (such as the risk/return tradeoff), the course contains an extensive module on strategic asset allocation with a focus on practical implementation. The course continues with an exposition of certain approaches to tactical asset allocation. The reminder of the course focuses on topics relevant to security selection and optimal portfolio construction. The course contains an extensive discussion of equity multi-factor models and screening, with applications to value and growth investing. The course highlights trends in the investment management industry and introduces terminology and tools familiar to investment professionals.
Prerequisite: NCC 5560. Prescribed self-study can substitute for this pre-requisite.
Case Studies (ORIE 5110)
Presents students with an unstructured problem that resembles a real-world situation. Students work in project groups to formulate mathematical models, perform computer analyses of the data and models, and present oral and written reports. Prerequisite: M.Eng. students in OR&IE.
Credit Risk (ORIE 5620)
Credit risk refers to losses due to changes in the credit quality of a counter party in a financial contract. This course is an introduction to the modeling and valuation of credit risks. Emphasis is on credit derivative instruments used for hedging credit risks, including credit swaps, spread options, and collateralized debt obligations.
Prerequisite: ORIE 3510.
Computational Methods in Finance (ORIE 5630)
This course covers computational techniques such as binomial trees, solution of PDEs, and Monte Carlo simulation for pricing financial instruments such as European and American options, path-dependent options, and bonds. Other computational topics such as delta and gamma hedging, Value at Risk, and portfolio problems will also be covered. The emphasis will be on implementation.
Prerequisite: ORIE M.Eng. students.
Other Electives
Advanced Corporate Finance (NBA 5400)
Relevant for both investment banking and the treasurer’s activities of an operating corporation. Most class sessions are lecture-discussion, but there will be several corporate finance cases. Topics include debt securities (duration, convexity, inverse floaters, bond refunding, term structure), convertible debt, capital structure, distribution policy, exotic new securities, financial strategies, and the buy versus lease decision. Investigates corporate financial policy decisions from a normative-quantitative point of view and develops skill in formulating financial models and evaluating models. Uses basic mathematics.
Prerequisite: NBA 5060 or equivalent.
International Finance (NBA 554)
Applies principles of finance to the international setting. International finance is different in two basic respects: (1) the existence of multiple currencies adds risk to investment and financing decisions; (2) when corporations and portfolio investors cross international borders, both problems and opportunities arise. This course focuses on these issues and highlights how finance theory can be extended to address them. Students apply the basic principles of international finance to a variety of problems. The course helps students understand the ideas and research results of international finance and adapt what they learn to the practical problems in the increasingly globalized business world. The first part of the course outlines exchange rate volatility, barriers to international capital flows, and the value of international diversification. The second part presents a variety of problems, examples, and applications from the three basic themes described in part one. Spreadsheet assignments and a term project requiring data analysis develop research skills and illustrate academic concepts. Exams consist of computational, short answer, and short essay questions.
Prerequisite: NCC 5060 (finance core) or permission of instructor.
ORIE 4740
Topics include multiple linear regression, diagnostics, model selection, inference, one and two factor analysis of variance. Theory and applications both treated. Use of MINITAB stressed.
Prerequisite: ENGRD 2700.
Applied Linear Statistical Models (ORIE 4710)
Topics include multiple linear regression, diagnostics, model selection, inference, one and two factor analysis of variance. Theory and applications both treated. Use of MINITAB stressed.
Prerequisite: ENGRD 2700.
Introduction to Game Theory (ORIE 4350)
Broad survey of the mathematical theory of games, including such topics as two-person matrix and bimatrix games; cooperative and noncooperative n-person games; and games in extensive, normal, and characteristic function form. Economic market games. Applications to weighted voting and cost allocation.
Quantitative Methods of Financial Risk Management (ORIE 5650)
A historical perspective of market risk measurement, including the Markowitz, CAPM, and APT models; investigation of the value-at-risk approach and its variants and extensions, and a survey of other methods for evaluating risk, including multivariate methods for evaluating portfolios requiring copula tools. Time permitting, we discuss approaches to measuring credit risk and determining default probabilities and company ratings based on financial ratios (logit, probit, and discriminant analysis, decision trees etc.). The software package S-PLUS is used. For 80% of the course, R or matlab could be used instead.
Prerequisites: ORIE 3500.
Applied Time Series Analysis (ORIE 5550)
Applied Time Series Analysis will explore the methods used in the analysis of numerical time series data. The course will be both theoretical and applied. Students will learn standard linear modeling concepts in the time and frequency domain, followed by some more recent topics such as nonlinear ARCH and GARCH models and possibly wavelets if time and student interest permits. Examples are provided throughout the instruction of the course, and students will implement the techniques discussed in class using real data sets. Dedicated students should come away with an in-depth understanding of statistical concepts related to time series, as well as a thorough comprehension of how and when to implement various techniques in practice. The course is designed for advanced undergraduates and beginning graduate students at the Masters level. Student from other disciplines are welcome to take the class, provided they have the sufficient mathematical and statistical backgrounds. Some experience in statistical computing is recommended.