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This page contains lecture notes from some of Marco Avellaneda's
courses at NYU from the mid 1990's.
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It contains, among other things, a full schedule of the New York University
Mathematical Finance Seminar , which takes place every Thursday and
is open to the public. Enjoy!

# Mathematics of Finance I

## Instructor: Marco Avellaneda

## Courant Institute of Mathematical Sciences

## Fall 1995, Fall 1996

This course covers the basic mathematical concepts
in derivative asset pricing. It provides a description
of the principal assets traded in financial markets
and then proceeds with an in-depth discussion of
Arbitrage Pricing Theory. The theory is applied
to the pricing options and
derivative securities in the contexts of binomial
probability trees and the Black-Scholes lognormal
model. The dynamical hedging of option
portfolios and of tailor-made financial derivatives is discussed.
I also cover American-style options,
interest-rate options and exotic options such as barrier options.

## Lecture Notes: Math Finance I

These lecture notes are in mostly in the form of book chapters. A
few consist of reproductions of trnsparencies used in the
lectures.
Syllabus Math Finance I and II

(also, a list of references)
Lecture #1

Derivative Securities: an Introduction (transparencies)
Lecture #2

Arbitrage Pricing Theory (transparencies)
Chapter1

Arbitrage Pricing Theory, I (10/9/96)
Exercises on one-period Arrow-Debreu model
(9/9/96)

Multi-period arbitrage pricing (preliminary)
(9/12/96

Chapter2

The binomial option pricing model
Chapter3

Analysis of the Black-Scholes Formula
Chapter4

Refinements of the binomial model and applications
Chapter5

American-style options, early exercise and time optionality
Lecture #6

Interest Rate Derivatives (transparencies)
Chapter6

Binomial Models for interest rate derivatives
Chapter7 (Revised)

Exotic Options, I ( Digitals and barrier options)

## Homework Assignments

Homework #1

Homework #2 New -- Fixed-income models

Homework #2

Homework #3
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