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)

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

The binomial option pricing model

Analysis of the Black-Scholes Formula

Refinements of the binomial model and applications

American-style options, early exercise and time optionality

Lecture #6
Interest Rate Derivatives (transparencies)

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

Back to Marco Avellaneda's main page

Back to the Courant Finance Server