2011-2012 Bulletin – PDF - SEAS Bulletin - Columbia University

OPERATIONS RESEARCH: FINANCIAL engineering:
Third and Fourth Years
165
Semester V Semester VI Semester VII Semester VIII
Required
Courses
ECON W3213 (3)
Macroeconomics
IEOR E3106 (3)
Stochastic models
IEOR E3608 (4)
Mathematical prog.
IEOR E4003 (3)
Industrial econ.
IEOR E3402 (4)
Production planning
IEOR E4404 (4)
Simulation
IEOR E4700 (3)
Intro. to FE
COMS W4111 (3)
Database systems
ECON W3211 (3)
Microeconomics
IEOR E4407 (3)
Game theoretic models
of operations
IEOR E4620 (3)
Pricing models for FE
IEOR E4500 (3)
Applications prog. for FE
IEOR E4630 (3)
Asset allocation
ECON E3412 (3)
Intro. to econometrics
Electives
financial
engineering
nontech
Choose three (9 pts.): Please consult the list on the departmental website: www.ieor.columbia.edu
Complete 27-point requirement; see page 10 or www.engineering.columbia.edu for details
IEOR E4630y Asset allocation
3 pts. Lect: 3. Professor Iyengar.
Prerequisite: IEOR E4700. Models for pricing
and hedging equity, fixed-income, creditderivative
securities, standard tools for hedging
and risk management, models and theoretical
foundations for pricing equity options (standard
European, American equity options, Asian
options), standard Black-Scholes model (with
multiasset extension), asset allocation, portfolio
optimization, investments over longtime
horizons, and pricing of fixed-income derivatives
(Ho-Lee, Black-Derman-Toy, Heath-Jarrow-
Morton interest rate model).
IEOR E4700x and y Introduction to financial
engineering
3 pts. Lect: 3. Professors He and Yao.
Prerequisite: IEOR E4106 or E3106. This course
is required for undergraduate students majoring
in OR:FE. Introduction to investment and financial
instruments via portfolio theory and derivative
securities, using basic operations research/
engineering methodology. Portfolio theory,
arbitrage; Markowitz model, market equilibrium,
and the capital asset pricing model. General
models for asset price fluctuations in discrete
and continuous time. Elementary introduction to
Brownian motion and geometric Brownian motion.
Option theory; Black-Scholes equation and call
option formula. Computational methods such as
Monte Carlo simulation.
IEOR E4701 Stochastic models for financial
engineering
3 pts. Lect: 3. Instructor to be announced.
Prerequisite: SIEO W4105. This course is for MSFE
students only, offered during the summer session.
Review of elements of probability theory, Poisson
processes, exponential distribution, renewal theory,
Wald’s equation. Introduction to discrete-time
Markov chains and applications to queueing theory,
inventory models, branching processes.
IEOR S4702 Statistical inference for financial
engineering
1.5 pts. Lect: 1.5. Professor Kou.
Corequisites: IEOR E4701 and E4706. This
course is for MSFE students only, offered during
the summer session. The course covers basic
tools of statistical inference relevant to financial
engineering. The statistical topics covered include
point estimation, maximum likelihood estimators,
confidence intervals, the delta method,
hypothesis testing, and goodness of fit tests.
The financial examples include selection bias in
finance, estimation of drift and volatility in the
geometric Brownian motion model, the leptokurtic
feature, and difficulties in estimating the tail
distributions of asset returns.
IEOR E4703y Monte Carlo simulation
3 pts. Lect: 3. Members of the faculty.
Prerequisite: IEOR E4701. This course is for
MSFE students only. Multivariate random number
generation, bootstrapping, Monte Carlo simulation,
efficiency improvement techniques. Simulation
output analysis, Markov-chain Monte Carlo.
Applications to financial engineering. Introduction
to financial engineering simulation software and
exposure to modeling with real financial data.
NOTE: Students who have taken IEOR E4404
Simulation may not register for this course for credit.
IEOR E4705x Studies in operations research
3 pts. Lect: 3. Professor Riccio.
Prerequisites: IEOR E4004 (or E3608) and IEOR
E4106 (or E3106). Analysis and critique of current
operations research studies. Blood bank inventory,
fire departments, police departments, and housing
operations research studies are considered.
IEOR S4706 Foundations of financial
engineering
3 pts. Lect: 3. Professor Cont.
Prerequisites: IEOR E4701, E4702, and linear
algebra. This course is for MSFE students only,
offered during the summer session. Discrete-time
models of equity, bond, credit, and foreignexchange
markets. Introduction to derivative
markets. Pricing and hedging of derivative
securities. Complete and incomplete markets.
Introduction to portfolio optimization and the
capital asset pricing model.
IEOR E4707x Financial engineering:
continuous-time asset pricing
3 pts. Lect: 3. Professor Haugh.
Prerequisites: IEOR E4701. This course is for
MSFE students only. Modeling, analysis, and
computation of derivative securities. Applications
of stochastic calculus and stochastic differential
equations. Numerical techniques: finite-difference,
binomial method, and Monte Carlo.
IEOR E4708y Seminar on important papers in
financial engineering
3 pts. Lect: 3. Professor Derman.
Prerequisites: IEOR E4703, E4706, probability
and statistics. Selected topics of special interest to
Financial Engineering M.S. students. If topics are
different then this course can be taken more than
once for credit.
engineering 2011–2012