Introductory Financial Mathematics, Fall 2018 

 
Instructor: Andrew Obus
email: Andrew.Obus [at] baruch.cuny.edu
office: VC 6-223
phone: 646-312-4008
website: http://faculty.baruch.cuny.edu/aobus/MTH4500f18.html

Lectures

MW 2:55-4:35, VC 13-150.  Please ask questions if anything in lecture is unclear. Lectures will run the entire 100 minutes.  I reserve the right to take attendance and to penalize those who do not show up.  I will certainly take attendance the first few classes in order to learn your names.  Furthermore, quizzes will take place at the beginning of class (see below), so it is imperative that you show up on time!

CELL PHONES MAY NOT BE TAKEN OUT IN CLASS --- I DO NOT WANT TO SEE THEM!  If you know that you are expecting an important call (relative in the hospital, etc.), you must let me know ahead of time.



Textbook

Mathematics for Finance, 2nd ed., by Marek Capiński and Tomasz Zastawniak.  This is a good book, but the level of mathematical sophistication is a bit uneven.  I will try to warn you when the math difficulty is going to pick up rapidly! You will find it extremely beneficial to read over the appropriate textbook sections before class.

Other books you may enjoy looking at are An Elementary introduction to Mathematical Finance by Sheldon M. Ross and Financial Calculus by Martin Baxter and Andrew Rennie (more mathematical).  The book Investments by William F. Sharpe, Gordon J. Alexander, and Jeffery V. Bailey is a good introduction to investing in general, not from a particularly mathematical perspective. I also highly recommend When Genius Failed, a popular and entertaining book by Roger Lowenstein about the Long Term Capital Management debacle and the crash of 1998.  This is a book you can easily read on the subway, in bed, in line at the DMV...


Content

This is a course on the mathematics underlying various aspects of finance, including but not limited to the pricing of options and other derivatives, culminating in the Black-Scholes formula.  We will also discuss the general problem of balancing risk and return, deriving the Capital Asset Pricing Model along the way.  In the last part of the course, we will introduce interest rate theory.  The most important concept will be that of arbitrage, or "something for nothing."  You can get a surprising amount of mileage out of this concept alone.  Indeed, many formulas we derive in this class will be different instances of the same underlying idea.

Note that we will be doing proofs in this class, and careful reasoning will be emphasized at every step. Don't be put off by the word "proof".  It just means a careful argument and explanation.  A primary goal of this class is for you to become comfortable making well-reasoned arbitrage-based pricing arguments in a variety of situations, while understanding what assumptions you are using in order for your reasoning to be valid.

Prerequisites: (MTH 3020 OR MTH 3030 OR MTH 3050) AND (MTH 3120 OR MTH 4120).  If you do not have these prerequisites, please see me immediately. 

If you fall too far behind in this course, it will be very difficult to catch up.  Please see me promptly if things stop making sense!


Office Hours

Mondays 4:35 - 5:35, Wednesdays 1:30 - 2:30, VC 6-223.  If these times do not work for you, please make an appointment with me.  I am also teaching MTH 2205 this semester.  You are welcome to come to either office hour, but MTH 2205 students will have priority during the Wednesday office hour.  MTH 4500 students will have priority during the Monday office hour.

NOTE:  On Wednesday 8/29, the office hour will be from 4:35 - 5:35, not from 1:30 - 2:30.


Homework and Quizzes

Homework will be assigned almost every week.  It will consist mostly of problems from the book perhaps with some small variations and additions.  Some questions may require a calculator.  The book gives short solutions to all of its problems, but it is important that you do them carefully and understand them in complete detail. 

Most weeks, there will be a short (10-15 minutes) in-class quiz on Wednesday inspired by (or drawn directly from) the homework, given at the beginning of class. The clarity of your writing will affect your quiz grade.

I may also assign occasional extra credit problems, which will be factored into your overall quiz grade.  You are encouraged to discuss homework and the extra credit problems with your classmates, but you must write up the solutions on your own.  There are no make up quizzes, but your lowest two quiz grades will be dropped.
 

Exams

Midterms will be in class on Wednesday 10/3 and Monday 11/5.  If you have a conflict with one of these days, you must let me know now.  The withdrawal deadline is 11/6, so I will put the grades for the second midterm on Blackboard no later than noon on 11/6.

The final exam is on Monday 12/17, from 3:30PM - 5:30PM.


Final Course Grades

20% Quizzes
23% Each midterm exam
34% Final Exam

Grading will be based on the Baruch grading scale.  It is possible for exceptional class participation to be factored into your numerical grade in borderline cases. 


Academic Honesty

Any cheating on exams or quizzes will result in a grade of 0 on the assignment involved.  Any cheating or plagiarism on extra credit problems will result in a grade of 0 for both the extra credit problem and for the quiz that week.  A second instance of cheating will result in automatic failure of the class.  Refer here for more information on Academic Honesty.


Disabilites

All students with special needs requiring accommodations should present the appropriate paperwork from Student Disability Services. It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.



Schedule (topics subject to change)

Class #
Date
Topics
Book Sections (approximate)
Remarks
1
8/27
Arbitrage, Binomial Model, Risk and Return
1.1 - 1.4

2
8/29
Forwards, Calls, Puts, Forex
1.5 - 1.8

3
9/5
Time Value of Money
2.1
Quiz 1
4
9/12
Money Market
2.2
Quiz 2
5
9/17
Risk and Return, Two Securities
3.1 - 3.2
Withdrawal gives W grade starting today.
6
9/24
Several Securities
3.3

7
9/26
CAPM
3.4
Quiz 3
8
10/1
Forwards
4.1

9
10/3
MIDTERM 1


10
10/10
Futures
4.2
Quiz 4
11
10/15
Put-Call Parity, Option Price Bounds 5.1 - 5.3

12
10/17
More Option Pricing, Time Value of Options
5.4 - 5.5
Quiz 5
13
10/22
One-Step Binomial Model
6.1 - 6.2

14
10/24
Multi-Step Binomial Model
6.2
Quiz 6
15
10/29
American and Exotic Claims
6.3

16
10/31
Hedging
6.5
Quiz 7
17
11/5
MIDTERM 2

Last class before withdrawal deadline.
18
11/7
Trinomial/General Tree Model
7.1 - 7.2

19
11/12
Fundamental Theorems of Asset Pricing
7.3 - 7.4

20
11/14
Black-Scholes Model
8.1 - 8.2
Quiz 8
21
11/19
Pricing Using Black-Scholes
8.4

22
11/21
Risk Management
8.5

23
11/26
Bonds: Maturity Independent Yields
9.1 - 9.2

24
11/28
Bonds: General Term Structure
9.3
Quiz 9
25
12/3
TBA
TBA

26
12/5
TBA
TBA
Quiz 10
27
12/10
TBA
TBA

28
12/12
Review for Final Exam
Quiz 11