2008-2009 Bulletin – PDF - SEAS Bulletin - Columbia University

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American equity options, Asian options), standard
Black-Scholes model (with multi-asset extension),
asset allocation, portfolio optimization, investments
over long-time horizons, and pricing of
fixed-income derivatives (Ho-Lee, Black-Derman-
Toy, Heath-Jarrow-Morton interest-rate model).
Note: Students may not take both IEOR E4630
and DRAN B8835.
IEOR E4700x and y Introduction to financial
engineering
Lect: 3. 3 pts. Professors Stoikov and Gallego.
Prerequisite: IEOR E3106 or IEOR E4106, or the
equivalent. 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 E4701s Stochastic models for financial
engineering
Lect: 3. 3 pts. Professor Sigman.
Prerequisite: SIEO W4105 or the equivalent.
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 E4702s Statistical inference for financial
engineering
Lect: 1.5. 1.5 pts. The faculty.
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 Iyengar.
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 E4706x 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. Professor Stoikov.
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
management, trading and technology in financial
markets.
IEOR E4724y or s Topics in quantitative
finance: hedge fund management
Lect: . 1.5–3 pts. Professor Metzger.
The course covers the critical managerial aspects
and characteristics of hedge funds and the hedge
fund industry, including legal regulations, strategies,
risk management, performance evaluation, etc.
IEOR E4725y or s Topics in quantitative
finance: numerical solutions of partial
differential equations
Lect: . 1.5–3 pts. Professor Kani.
The course covers derivations and solutions of
partial differential equations under a 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 or s Topics in quantitative
finance: experimental finance
Lect: . 3 pts. Professor Stanton.
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 will
become familiar with computational techniques for
modeling and testing proposals for trading strategies.
IEOR E4731y Credit derivatives
Lect: 2.5. 3 pts. Professor Cont.
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, arbitrage pricing, default times,
single-name credit derivatives, structured models
for single-name credit risk, multi-name default
barrier models and multi-name reduced form
models.
SEAS 2008–2009