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Core Courses
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| MTH 9814 A Quantitative Introduction to
Pricing Financial Instruments |
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This course presents some of the most important derivative
securities traded in the financial markets: forward and futures contracts,
swaps, and options. Pricing principles such as arbitrage pricing, risk
neutral pricing, the Black-Scholes formula and binomial trees are studied.
Credit Risk and Credit Risk derivatives are also discussed.
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| MTH 9815 Object Oriented Programming for
Financial Applications |
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This course covers the general and advanced features of
object oriented programming and their
applications to solving financial engineering problems. Topics include:
Template Programming in C++, Encapsulation, Inheritance and Virtual
Functions, Bridging with a Virtual Constructor, Design
Patterns, Programming in the Black-Scholes Environment.
Co-requisite: MTH 9814.
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| MTH 9821 Numerical Linear Algebra (core math
course) |
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This course begins with a brief presentation of fundamental
linear algebra topics: vector spaces,
eigenvalues and eigenvectors, and diagonal forms of matrices. The main part
of this course consists of the study of numerical methods used in linear
algebra: direct and iterative methods for solving linear systems, eigenvalue
methods, least square problems, and Newtons method.
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| MTH 9831 Real Analysis and Probability (core
math course) |
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This course covers enough measure and integration theory to
lead quickly to probability. The fundamentals of probability are then
covered, to include probability spaces, random variables, expectation,
conditional probability and expectation, moments and certain limit theorems.
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| MTH 9852 Numerical Methods for PDEs in
Finance (core math course) |
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Security prices are often represented as solutions to
parabolic partial differential equations (PDEs)
arising out of the stochastic calculus. This course focuses on the study of
these equations, from both a theoretical and a numerical point of view.
Several finite difference methods are presented, and their performance is
compared with other methods, e.g., binomial methods. Applications include
the Black-Scholes formula for American options as the solution of a PDE as
well as some exotic option pricing. Prerequisites: MTH 9815, MTH 9821, MTH
9831.
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| MTH 9862 Stochastic Processes in Finance
(core math course) |
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This course covers the basic stochastic processes and
probabilistic techniques used in finance,
for example: random walks, Markov chains, martingales, Brownian Motion,
stochastic integration, and Itô's formula. The Black-Scholes formula is
presented from the standpoint of expectation in
an appropriate probability space. Prerequisites: MTH 9815, MTH 9821, MTH
9831.
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| MTH 9871 Advanced Computational Methods in
Finance |
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This course covers the various specialized mathematical
numerical methods that are applied to security valuation and risk
management. The mathematical principles of arbitrage-free valuation are
applied to binomial and other lattice methods, term structure interest rate
models, path-dependent securities, multi-factor models, Monte Carlo methods,
and other current topics. Prerequisites: MTH 9852, MTH 9862.
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| MTH 9873 Interest Rate Models and Interest
Rate Derivatives |
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This course covers aspects of interest rate modeling and the
valuation of fixed-income securities.
Interest rate models such as Ho-Lee, Hull-White, Black-Derman-Toy, and
Black-Karasinski will be
presented. Topics include: implied volatility and mean reversion,
path-dependent securities, option
adjusted spread, duration and convexity, hedging techniques, Monte Carlo
methods, and multi-factor models.
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| MTH 9903 Capstone Project and Presentation |
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Each student is required to prepare a case study motivated
by a real-world problem in finance whose solution requires the application
of mathematical techniques presented in this program. The students analysis
and conclusions are presented to faculty and students.
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| Electives
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| MTH 9841 Statistics for Finance |
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This course will cover probability and statistics form
a Bayesian perspective, with applications to finance. Topics will include
joint marginal and conditional probability; discrete and continuous random
variables; Bayesian inferences for means and proportions compared with the
corresponding frequentist ones; simple linear regression model analyzed in a
Bayesian manner; Bayesian approach to portfolio optimization, including
Black-Litterman. A portion of the course will be devoted to teaching a
statistical package, most likely R or S-Plus.
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| MTH 9842 Linear and Quadratic Optimization
Techniques |
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This course covers linear and quadratic optimization
as well as other nonlinear techniques. Applications from finance include
problems in game theory and portfolio optimization. Prerequisites: MTH 9821,
MTH 9831. Corequisite: MTH 9815.
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| MTH 9848 Elements of Structured Finance |
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The course objective is to allow students to analyze the
basic credit quality of securitizations backed by commodity asset types
(mortgages, auto loans, credit cards, CDOs). Mastery of the material in this
course will let the student model and evaluate the credit impact of
collateral or structural alternatives. Hands-on work is both extensive and
preparatory to the advanced level.
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| MTH 9849 Deal Theory and Structured Analysis |
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After taking this class, successful candidates will be able
to model a transaction a priori based on the prospectus and issuer databases
using the techniques described in class. In addition, the student will be in
a position to accurately value asset-backed securities in arbitrary
non-revolving transactions in most asset classes, i.e. to assign them assign
credit ratings and interest rates. It is also an objective to enable
students to discuss intelligently the drivers of credit, liquidity and other
risks with a view towards optimal liability structuring.
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| MTH 9845 Market and Credit Risk Management |
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This course covers qualitative and quantitative aspects of
the financial risk associated with managing financial portfolios and with
credit default. Topics include: market risk, VaR and stress testing, model
risk, spot and forward risk, credit default risk and credit derivatives.
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| MTH 9881 Current Topics in Mathematical
Finance |
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Students are assigned current journal articles in
financial mathematics for discussion in a seminar format.
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