## Lecture-by-lecture Topics and Assignments  Math 495 -- Fall 2006

This page will record the topics we cover, with links to problem sets and handouts. Please read the relevant sections of the course text by Stampfli and Goodman before the lecture in which it is discussed. Reserve reading is strongly suggested.
1, 9/5 Financial Markets and derivatives;
Introduction to binomial models
One bond/one-stock model; Forward contracts
Text: 1.1-1.3, 1.6
Reserve: Hull, Chapter 1
Lecture 1 outline(pdf file)
Corrections to lecture 1 outline
Problems
2, 9/7 No arbitrage pricing of forward contracts; no arbitrage in the one-period model
Text: 1.2,1.3, 2.1
Reserve, Hull, pp. 99-109 Lecture 2 outline(pdf file)
Problems
3, 9/12 More on no-arbitrage pricing
of forward contracts and in one-period models
Read Lecture 2 outline(pdf file) before coming to class!

4, 9/14 Replicating portfolio principle;
Valuing forward contracts, put-call parity;
pricing derivatives in the one-period binomial model
Text: Chapter 2 Problems for lectures 3,4
5, 9/19 The one period binomial model; risk-neutral measure and
the fundamental theorem of asset pricing, I.
Text, Chapter 2 and Lectures 4-5 notes.
6, 9/21 The risk neutral measure and pricing by expectation Class notes
7, 9/26; Introduction to multi-period binomial trees Text, sections 3.1, 3.2, 3.3
Problems
8, 9/28 Multi-period tree models continued Text, 3.4, 3.5, and class notes Lecture 8 notes
Hull, Chapter 11.

9, 10/3 Expectation and the risk-neutral measure Class notes--see lecture 8
10, 10/5 Conditional expectation Class notes
11, 10/10 Recitation lecture
12, 10/12 Pricing by conditional expectations, portfolio processes
no arbitrage in binomial tree model
Class notes to appear
13, 10/17 FIRST MIDTERM, IN CLASS!
14, 10/19 Conditional expectations and applications to pricing Class notes
15, 10/24 Conditional expectations, pricing and martingales Lecture Notes
16, 10/26 Martingales and portfolios
17, 10/31 Portfolio replication
Central Limit Theorem
Notes on portfolio replication
Notes on normal r.v.'s and the Central Limit Theorem
See problems page for homework due on 11/2
18, 11/2 Brownian motion Class Notes on Brownian motion
19, 11/7 Brownian motion and the Black-Scholes model
20, 11/9 Brownian motion and the Black-Scholes model Chapter 4, Models, pricing and Black-Scholes pricing
21, 11/14 The Black-Scholes model Chapter 5
22, 11/16 Black-Scoles, estimating parameters, calculating prices, deriving the Black-Scholes formula Chapter 5, Lecture notes on binomial tree approximation
23, 11/21 Black-Scoles, continued
24, 11/28 Midterm II
25, 11/30 Ito calculus introduction Chapter 6, Class notes; Intro to Ito calculus
26, 12/5 The Black-Scholes pde, hedging, and the greeks Chapters 6 and 7, Ito calculus and Black-Scholes
27, 12/7 The Black-Scholes pde, hedging, and the greeks, continued Chapters 6 and 7, Portfolio analysis with the greeks
28, 12/12 The Black-Scholes pde, hedging, and the greeks, continued Chapters 6 and 7, More about Black-Scholes and the Greeks