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FRE 6083  Quantitative
Methods in Finance
Frederick Novomestky, Ph.D.
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Course Objectives
The first part of this course focuses on the art and
science of building models of processes that
occur in finance, economics, and the social
sciences in general.
These may include models
of aggregate economic activity or the behavior of
asset prices.
We do not attempt to cover the
spectrum of model types and modeling
methodologies; rather, the focus is on models
that can be expressed in equation form, relating
variables quantitatively. The primary focus is on
the use of calculus, linear algebra and probability
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Course Objectives
Data are then used to estimate the parameters of
the equation or equations, and theoretical
relationships are tested statistically.
Software
tools like Excel and R are used for empirical
work.
R is a language and environment for statistical
computing and graphics.
It is a GNU project (e.g.,
Open Source) which is similar to the SPlus
language developed at Bell Laboratories.
Download version from
www.rproject.org
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Course Objectives
The second half of the course develops the theory
of discrete and continuoustime stochastic
models as applied to the valuation of options and
other derivative securities.
Brownian motion,
Markov chains, Markov process, Poisson process
and related stochastic processes, stochastic
integration, Itô's formula, and other aspects of
stochastic calculus are treated with substantial
rigor.
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Course Objectives
This includes the derivation and solution of the
differential equation leading up to the Black
Scholes model for pricing stocks.
The theory is
balanced with concrete numerical applications.
Basic Monte Carlo simulation techniques will be
used in additional to analytical methods.
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Textbooks and Grading
Textbooks and Software
É
Nefcti, Mathematics of Financial Derivatives
É
Ross, Probability Models
É
Papoulis, Probability and Random Processes
É
R
Grading
É
30% Midterm
É
30% Final
É
10% Classroom Participation
É
30% Homework
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
The Axioms of Probability
Set Theory
Probability Space
Conditional Probabilities and Independent Events
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Set Theory
A review of notation and basic set theoretic options
is covered in the file SetTheoryReviewSlides.pdf.
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Probability Spaces
Definitions
Trials
The Axioms of Probability
Fields
Events
Definition of an Probability Space
Construction of Probability Spaces
Probabilities on the Real Line
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FRE 6083 Quantitative Methods in Finance  Copyright F. Novomestky 2007
Probability Spaces  Definition
A probability space is an ordered triple.
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This note was uploaded on 02/16/2011 for the course FE 6083 taught by Professor Neveskyi during the Spring '11 term at NYU Poly.
 Spring '11
 Neveskyi

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