Hello surfers!
This page contains lecture notes from some of Marco Avellaneda's
courses at NYU from the mid 1990's.
If you have arrived here first, you may want to visit the
Courant Finance
Server , a large site dedicated to serving papers, software and
tutorials
in quantitative finance. CFS is maintained and updated on a regular basis.
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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