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

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IEOR E4709x Data analysis for financial
engineering
3 pts. Lect: 3. Professor Kou.
Prerequisites: Probability and IEOR E4702.
Corequisites: IEOR E4706, E4707. This course is
for MSFE students only. 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
3 pts. Lect: 3. Professor Haugh.
Prerequisites: IEOR E4706, E4707, and computer
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
3 pts. Lect: 3. Professor Derman.
Prerequisites: IEOR E4706, knowledge of
derivatives valuation models. During the past 15
years the behavior of market options prices have
shown systematic deviations from the classic
Black-Scholes model. The course examines
the empirical behavior of implied volatilities, in
particular the volatility smile that now characterizes
most markets, the mathematics and intuition
behind new models that can account for the smile,
and their consequences for hedging and valuation.
IEOR E4720x and y–E4729 Topics in
quantitative finance
1.5–3 pts. Lect: 2–2.5. Members of the faculty.
Prerequisites: IEOR E4700; additional prerequisites
will be announced depending on
offering. Selected topics of interest in the area
of quantitative finance. Offerings vary each
year; some topics include: 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
management, trade and technology in financial
markets.
IEOR E4725y Topics in quantitative finance:
numerical solutions of partial differential
equation
3 pts. Lect: 3. Not offered in 2011–2012.
Prerequisites: IEOR E4706 and E4707.
The course covers derivations and solutions
of partial differential equations under variety of
underlying stochastic price processes. Students
will gain exposure to applications of partial
differential equations to security pricing in different
financial markets (i.e. equity derivatives, fixed
income securities and credit derivative markets).
IEOR E4726y Topics in quantitative finance:
experimental finance
3 pts. Lect: 3. Professors Lipkin and Stanton.
Prerequisites: IEOR E4706 and E4707. The
course introduces concepts to propose trading
schema, organize tests via options/stock
databases and carry out tests efficiently and
accurately. It exposes students to the striking
differences between static, thermodynamic/
SDE model solutions and real (time-of-flight)
pricing. They become familiar with computational
techniques for modeling and testing proposals for
trading strategies.
IEOR E4729 Financial markets, risk, and
institutions
1.5 pts. Lect: 1.5.
Corequisites: IEOR E4701, E4702, E4706.
This course is for MSFE students only, offered
during the summer session. This core curriculum
course introduces students pursuing a graduate
degree in financial engineering to the main
areas and concepts of modern finance. Topics
include financial analytics; fixed income and
equity markets; macroeconomic aspects of
investment decisions; portfolio and utility
theories; introduction to risk management;
financial crises. The course’s objective is to
provide the broadest possible perspective
on how financial theory and real-life practice
interact, preparing students for successful
careers in the financial industry and paving the
way for in-depth studies that follow.
IEOR E4731y Credit risk modeling and credit
derivatives
3 pts. Lect: 3. Instructor to be announced.
Prerequisites: IEOR E4701 and E4707.
Introduction to quantitative modeling of credit risk,
with a focus on the pricing of credit derivatives.
Focus on the pricing of single-name credit
derivatives (credit default swaps) and collateralized
debt obligations (CDOs). Detail topics include
default and credit risk, multiname default barrier
models and multiname reduced form models.
IEOR E4900x and y Master’s research or
project
1–3 pts. Members of the faculty.
Prerequisite: Approval by a faculty member who
agrees to supervise the work. Independent work
involving experiments, computer programming,
analytical investigation, or engineering design.
IEOR E4998x and y Managing technological
innovation and entrepreneurship
3 pts. Lect: 3. Professor McGourty.
This is a required course for undergraduate
students majoring in OR:EMS. Focus on the
management and consequences of technologybased
innovation. Explores how new industries
are created, how existing industries can be
transformed by new technologies, the linkages
between technological development and the
creation of wealth and the management challenges
of pursuing strategic innovation.
IEOR E4999x and y Curricular practical
training
1–2 pts. Professor Derman.
Prerequisites: Obtained internship and approval
from faculty adviser. Only for IEOR graduate
students who need relevant work experience
as part of their program of study. Final reports
required. This course may not be taken for pass/
fail credit or audited.
MSIE W6408y Inventory theory
3 pts. Lect: 3.
Prerequisites: Probability theory, dynamic
programming. Construction and analysis of
mathematical models used in the design and
analysis of inventory systems. Deterministic and
stochastic demands and lead times. Optimality
of (s, S) policies. Multiproduct and multiechelon
systems. Computational methods.
IEOR E6602y Nonlinear programming
3 pts. Lect: 3.
Prerequisite: Ph.D.-level linear programming.
Convex sets and functions, convex duality and
optimality conditions. Computational methods:
steepest descent, Newton and quasi-newton
methods for unconstrained problems, active set,
penalty set, interior point, augmented Lagrangian
and sequential quadratic programming methods
for constrained problems. Introduction to
nondifferentiable optimization and bundle methods.
IEOR E6613x Optimization, I
4.5 pts. Lect: 3. Professor Goldfarb.
Prerequisite: Linear algebra. Theory and geometry
of linear programming. The simplex method.
Duality theory, sensitivity analysis, column
generation and decomposition. Interior point
methods. Introduction to nonlinear optimization:
convexity, optimality conditions, steepest descent,
and Newton’s method, active set, and barrier
methods.
IEOR E6614y Optimization, II
4.5 pts. Lect: 3. Professor Stein.
Prerequisite: Linear algebra. An introduction to
combinatorial optimization, network flows and
discrete algorithms. Shortest path problems,
maximum flow problems. Matching problems,
bipartite and cardinality nonbipartite. Introduction
to discrete algorithms and complexity theory:
NP-completeness and approximation algorithms.
IEOR E6703y Advanced financial engineering
3 pts. Lect: 2. Not offered in 2011–2012.
Prerequisites: Probability theory and advanced
stochastic models at the SIEO W6501 level.
Review of basic mathematics, including renewal
theory and stochastic calculus. Martingale
approach to Black-Scholes formula. Optimal
stopping and American options. Pricing of
continuous and discrete exotic options. Term
structure models and pricing of bond options.
Jump diffusion models. Applications, including
pricing of real and electricity options and hedging
of real options.
IEOR E6711x Stochastic models, I
4.5 pts. Lect: 3. Professor Olvera-Cravioto.
Prerequisite: SIEO W4105 or equivalent. Advanced
treatment of stochastic modeling in the context
of queueing, reliability, manufacturing, insurance
risk, financial engineering and other engineering
engineering 2011–2012