# MATH 210

## Instructor

• Stephen Kleene
Lectures: MW 2:00-3:15 p.m. at Gavett 310
Office: Hylan 1011
Office Hours: M 9:25-10:25 a.m. and F 10:00 – 11:00 a.m.
E-mail: skleene at ur dot rochester dot edu

### Prerequisites

FIN 205 and (MTH 143 or 162) and (one of STT 211, 212, 213, ECO 230, or MTH 201).

## Course description

Mathematical concepts and techniques underlying finance theory; arbitrage pricing theory and option pricing. The emphasis will be on methods and proofs, rather than on plugging numbers into formulas.

### Textbook and Lecture Notes

Textbook: An Introduction to Quantitative Finance by Stephen Blyth

Lecture notes by Kyle Hambrook.

You will find that the lectures and lecture notes very closely match the presentation of the textbook, except with more examples, more exercises, and more thorough explanations. The lecture notes also contain background material on probability theory that the textbook does not.

### Other Resources

Here is a table to find values of Phi (standard normal cdf):

Table of Values for Phi (Standard Normal CDF)

Example for Table: Phi(1.96) is the value in row 1.9 and column 0.06.

Here is a widget to find probabilites for the normal distribution, including values of Phi (standard normal cdf).

Example for Widget: The input to Calculate Phi(1.96) is

• mean = 0
• standard deviation = 1
• a = -infty
• b = 1.96

One can also access the widget using this link. Here are links for another app to find probabilites for the normal distribution, including values of Phi (standard normal cdf). It works for other distributions as well, and it has IOS and Andriod versions for your phone.

Final Grade = 20% Homework + 35% Midterm Exam + 45% Final Exam

If it would result in a higher final grade for you, your final exam will be worth 80% and your midterm will be worth 0%. This will be done automatically.

• 93-100 A
• 90-93 A-
• 87-90 B+
• 83-87 B
• 80-83 B-
• 77-80 C+
• 73-77 C
• 70-73 C-
• 67-70 D+
• 63-67 D
• 60-63 D-
• 0-60 E

We will always round up at the borders.

### Homework

• Homework will be due Sundays at 11:59pm submitted through gradescope.
• Homework assignments and due dates will be posted on Sunday a week before.
• No late submissions will be allowed.

### Midterm Exam

• Date, Time, Location: Monday, March 6, at 2:00-3:15 in class
• Duration: 75 minutes
• No notes, textbooks, calculators, phones, or other electronic devices.
• No accommodation for missing the midterm will be given.

### Final Exam

• Date, Time: TBA Location: TBA
• Duration: 3 hours
• No notes, textbooks, calculators, phones, or other electronic devices.
• No make-up final exam will be given.

You should know and be able to work with the main ideas of the course. For example, you may be asked to: State a definition or prove a result from class; Solve a problem similar to a class example or homework exercise; Solve a problem that is somewhat different from what you’ve seen in class and homework, but that still uses the concepts we have studied.

A sample exam will be posted about a week in advance of the midterm and final.

All assignments and activities associated with this course must be performed in accordance with the University of Rochester’s Academic Honesty Policy.

You may work together on homework, but copying on homework or exams is NOT allowed, and it will be considered academic dishonesty.

Math Study Hall, Tutoring, and Other Resources

Work with your classmates (but don’t copy assignments). It is essential to not fall behind because each lecture is based on previous work. If you are having any difficulties, seek help immediately.

### Disability Resources

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of a disability, please contact the Office of Disability Resources. The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations.

Office of Disability Resources (disability@rochester.edu; (585)275-9049; 1-154 Dewey Hall)

To be granted alternate testing accommodations, you (the student) must fill out forms with the Office of Disability Resources at least seven days before each and every exam. These forms are not sent “automatically.” Professors are not responsible for requesting alternative testing accommodations at the Office of Disability Resources, and they are not obligated to make any accommodations on their own.

: HW1 Solutions
HW2 Solutions
HW3 Solutions
HW4 Solutions

### Schedule

Below is the approximate schedule of the class. Textbook and lecture notes reading is listed by section number.

Week 1 (Week of Jan 22)
Topics: Basic probability
Lecture Notes Reading: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3

Week 2 (Week of January 29)
Topics: Monotonicity and replication, Interest rates and compounding, Zero coupon bonds and discounting, Time value of money
Textbook Reading: 6.2, 1.1, 1.2, 1.3
Lecture Notes Reading: 2.4, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6,

Week 3 (Week of February 5)
Topics: Annuities, Stocks, Bonds, Foreign exchange, Derivative contracts, Forward contracts, Forward on asset paying no income
Textbook Reading: 1.3, 1.5, 2.1, 2.2, 2.3
Lecture Notes Reading: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6

Week 4 (Week of February 12)
Topics: Forward on asset paying known income, Value of forward contract, Forward on stock paying dividends and on currency
Textbook Reading: 2.4, 2.5, 2.6, 2.7
Lecture Notes Reading: 4.7, 4.8, 4.9, 4.10

Week 5 (Week of February 19)
Topics: Forward zero coupon bond prices, Forward interest rates, Libor, Forward rate agreements and forward libor, Value of floating and fixed cashflows
Textbook Reading: 3.1, 3.2, 3.3, 3.4, 3.5
Lecture Notes Reading: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7

Week 6 (Week of February 26)
Topics: Swap definition, Forward swap rate and swap value, Spot-starting swaps, Swaps as difference between bonds
Textbook Reading: 4.1, 4.2, 4.3, 4.4
Lecture Notes Reading: 6.1, 6.2, 6.3. 6.4, 6.5, 6.6

Week 7 (Week of March 4)

: Midterm 1 is on Wednesday, March 6 in class. It is closed book, closed notes exam. It covers everything up to and including what we have covered before Spring break.

Topics: Physical versus cash settlement, Futures definition, Futures versus forward prices, Option definitions, Put-call parity

Textbook Reading: 2.8, 5.1, 5.2, 7.1, 7.2
Lecture Notes Reading: 7.1, 7.2, 7.3, 7.4, 7.5, 8.1, 8.2, 8.4, 8.5

Week 8 (Week of March 11)

: Spring Break

Week 9 (Week of March 18)
Topics: Bounds on call prices, Call and put spreads, Call butterflies, Digital options
Textbook Reading: 7.3, 7.4, 7.5, 7.6
Lecture Notes Reading: 8.6, 8.7, 8.8, 8.9, 8.10, 8.11, 8.12, 8.13

Week 10 (Week of March 25)
Practice Midterm.
Practice Midterm Solutions.
Topics: Some advanced probability, Binomial Tree
Lecture Notes Reading: 9.1, 9.2, 9.3, 10.1, 10.2

Week 11 (Week of April 1)
Topics: Binomial Tree, Fundamental Theorem of Asset Pricing
Textbook Reading: 8.1, 8.2, 8.3, 8.4, 10.1
Lecture Notes Reading: 10.2, 10.3, 10.4, 10.5, 10.6

Week 12 (Week of April 8)
Topics: Normal distribution and central limit theorem, Black-Scholes model
Lecture Notes Reading: 11.1, 11.2, 12.1, 12.2, 12.3, 13.1, 13.2, 13.3

Sahra Karakoc’s presentation of CLT

Week 13 (Week of Apr 15)
Topics: Properties of Black-Scholes model, Delta and Vega, Volatility