2009-2010 Bulletin – PDF - SEAS Bulletin - Columbia University

OPERATIONS RESEARCH: THIRD AND FOURTH YEARS
161
SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII
MATH E1210 (3) IEOR E3402 (4) IEOR E4307 (3) IEOR E4405 (3)
Ordinary diff. equations Production planning Forecasting Prod. scheduling
REQUIRED
COURSES 1
IEOR E3608 (4) IEOR E4404 (4) IEOR E4003 (3)
Mathematical prog. Simulation Industrial econ.
IEOR E3106 (3) IEOR E4600 (3) IEOR E4407 (3)
Stochastic models Applied integer prog. Game theoretic models
of operations
IEOR E4409 (3)
Industrial info. sys.
TECHNICAL
ELECTIVES
Choose four electives (12 pts. total):
Please consult the list on the departmental Web site: www.ieor.columbia.edu
NONTECH
ELECTIVES
Complete 27-point requirement. See page 11 or www.engineering.columbia.edu for details
1 Taking required courses later than the prescribed semester is not permitted.
IEOR E4702s Statistical inference for financial
engineering
Lect: 1.5. 1.5 pts. Professor Kou.
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 E4703x Monte Carlo simulation
Lect: 3. 3 pts. Professor Blanchet.
Prerequisite: IEOR E4701 or the equivalent.
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 may not register for this course.
IEOR E4705x Studies in operations research
Lect: 3. 3 pts. Professor Riccio.
Prerequisites: IEOR E3608 (or E4004) and 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 E4706s Foundations in financial
engineering
Lect: 3. 3 pts. Professors Kou and Tilman.
Prerequisites: SIEO W4150 and linear algebra
(MATH V2010 or APMA E3101). Corequisites:
IEOR E4701 and E4702 or their equivalents.
Bond mathematics. Introduction to forwards, futures,
and other derivative securities. Discrete-time
models of equity markets and the term structure.
Pricing and dynamic hedging of derivative securities.
Option pricing and Black-Scholes, introduction
to real options and portfolio optimization.
IEOR E4707x Financial engineering: continuoustime
asset pricing
Lect: 3. 3 pts. Professor Cont.
Prerequisite: IEOR E4701. Corequisite: IEOR
E4706. 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 classical and new
papers in financial engineering
Lect: 3. 3 pts. Professor Derman.
Prerequisites: IEOR E4701 and E4706.
Corequisite: IEOR E4703. 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.
IEOR E4709y Data analysis for financial
engineering
Lect: 3. 3 pts. The faculty.
Prerequisite: IEOR E4701. Corequisite: IEOR
E4706. Empirical analysis of asset prices: heavy
tails, test of the predictability of stock returns.
Financial time series: ARMA, stochastic volatility,
and GARCH models. Regression models: linear
regression and test of CAPM, nonlinear regression
and fitting of term structures.
IEOR E4710y Term structure models
Lect: 2. 3 pts. The faculty.
Prerequisites: IEOR E4706, E4707, and proficiency
in programming. Interest rate models and numerical
techniques for pricing and hedging interest rate
contracts and fixed income securities.
IEOR E4718y Introduction to the implied
volatility smile
Lect: 3. 3 pts. Professor Derman.
Prerequisite: IEOR E4706 or some knowledge of
derivatives valuation models. During the past fifteen
years the behavior of market options prices have
shown systematic deviations from the classic
Black-Scholes model. The course will examine the
empirical behavior of implied volatilities, in particular
the volatility smile that now characterizes most
markets, and then discuss the mathematics and
intuition behind new models that can account for
the smile, and then examine their consequences
for hedging and valuation.
IEOR E4720-E4729s and y Topics in quantitative
finance
Lect: 2–2.5. 1.5–3 pts. The faculty.
Selected topics of interest in the area of quantitative
finance. Offerings vary each year; possible
topics include asset management, energy derivatives,
experimental finance, foreign exchange and
related derivative instruments, inflation derivatives,
hedge fund management, modeling equity
derivatives in Java, mortgage-backed securities,
numerical solutions of partial differential equations,
quantitative portfolio management, risk
SEAS 2009–2010