Spring 2006
Math 4490
– Mathematics of Financial derivatives
|
Date |
Section |
Assignment |
|
Jan 9 |
Introduction
to options and other financial derivatives (Lect.1) |
See problems at the end
of Lecture 1. HW#1: Ex. 8, 9, 10,
12. |
|
Jan 11 |
One
step securities markets (Lect.2) |
See exercises at the end
of Lecture 2. HW#1: Ex. 3, 4. |
|
Jan 16 |
No class. MLK holiday |
|
|
Jan 18 |
Valuation of contingent claims. More on risk neutral probability measures (Lect.3) |
|
|
Jan 23 |
Valuation of contingent
claims. One step in the Binomial Model. |
HW#1 due HW#2:
Ex. 1,2,3 at the end of Lecture 3. HW#2 to be continued |
|
Jan 25 |
The
Binomial Model (Lect.4) I made a few modifications to lecture 4. |
HW#2: Ex. 1,2,3
Lecture 4. See problems from above as well. |
|
Jan 30 |
HW#2 due postponed until
Monday, Feb 6. |
|
|
Feb 1st |
Brief
overview of Probability. (Lecture 6) See also link on Joint
probability distributions and Random samples. |
See Ex. 1,2 at the end of Lecture 5. Work the exercises at
the end of Lecture 6. They are due next week. |
|
Feb 6 |
Introduction to
stochastic processes. The
Brownian Motion. (Lecture 7) Brownian
Motion applet. Another
one. |
Bring in HW#2. HW#3.
Ex. 1,2,3,5,6,7 (Lecture 6) Note that
there was an omission in Ex 5. I had it fixed. |
|
Feb 8 |
HW#3 due (postponed
until Monday, Feb 13) |
|
|
Feb 13 |
Topics in Riemann integral and Stieltjes integral. |
Find more facts about
the Brownian motion on the Internet and other sources. Read Sections 2.1 and
2.2 from Kerry Back |
|
Feb 15 |
Construction
of the Itô stochastic integral. |
|
|
Feb 20 |
Discussing
the problems in Exam 1 |
See Lecture 8. Work exercises on
Lecture 8. HW will be posted soon. |
|
Feb 22 |
Computing stochastic integrals. (Lecture 9) |
HW#4. Ex.
3, 5 Lecture 8 |
|
Feb 27 |
|
|
|
March 1st |
Functions with unbounded variation. See the maple file on Stieltjes integral. I added a routine that computes the total variation of a function on a given interval for a given partition. Itô’s Lemma (differentiation like you’ve never seen before- Lecture 10). |
HW#4 due |
|
March 13 |
Itô’s Lemma. |
HW#4 due Start working problems
in Lecture 10. |
|
March 15 |
The geometric Brownian motion. (Lecture 11) |
Try to prove Holder’s
inequality using the hint I gave in class. Work exercises in
Lecture 10. |
|
March 20 |
The distribution of the stock price
(Maple file) The lognormal distribution of the stock
price (Lecture 12) |
HW#5: Ex
1-7 Lecture 10.
Ex 1-4 Lecture 11. Review computation of
normal probabilities. Read review on Point
estimation and confidence intervals on Resources page. |
|
March 22 |
HW#5 due |
|
|
March 27 |
Using the Black-Scholes formula.(Lecture 13) |
|
|
March 29 |
Problem
solving |
Read (
I mean it) Sections 4.2-4.7 in Back. |
|
April 3rd |
Problem 4.1 Back (Minitab project
file) |
Ex. 4.1 Back. Read section 12.13 on
Dividends in handout from Work ex: 12.2, 12.4,
12.5,12.13, 12.15.
|
|
April 5 |
American call with dividends
(Maple file) |
Finish problem 12.15. |
|
April 10 |
|
HW#6
Finish the analysis on problem 12.15. Compute V(ln(S_T)) in problem 4.1 Back (we started some computation
in class) Also: ex 12.2, 12.4,
12.14. |
|
April 12 |
Risk-free interest rate (Maple
file) |
HW#6 due |
|
April 17 |
Project
discussions |
|
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April 19 |
Project
discussions |
|
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April 21 |
Project
discussions and presentations |
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April 24 |
Project discussions and presentations |
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April 26 |
Capstone presentations: Congratulations
to all presenters! |
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April 27 |
Exam #2 – the exam is due May 3rd by |
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