## Math 210 - Introduction to Financial Mathematics

### Instructors

Kyle Hambrook
Lectures: MW 15:25-16:40 LATT 201
E-mail: kyle dot hambrook at rochester dot edu
Office: Hylan 905
Office Hours: Mon Wed 12:00 – 1:00, 5:00 – 6:00, or by appointment.
Carl Mueller
Lectures: MW 12:30-13:45 MOREY 321
E-mail: carl dot e dot mueller at rochester dot edu
Office: Hylan 802
Office Hours: Mon 2:00 - 3:30, Tues 10:30 - 12:00

Note: Office hours of all instructors are open to all MTH 210 students, regardless of which section they are registered for.

### TAs

Xinyi Fan
E-mail: xfan6 at u dot rochester dot edu
Office Hours: Tues 12:30-1:30, 2nd floor of Carlson
Dabid Hyowang Kim
E-mail: dkim79 at u dot rochester dot edu
Office Hours: Tues 2:00-3:00, Carlson, near room 102
HaoKun Liu
E-mail: hliu39 at u dot rochester dot edu
Office Hours: Tues 1:00-2:00, main floor of Rush Rhees
Kathy Luo
E-mail: jluo12 at u dot rochester dot edu
Office Hours: Tuesday 10:00-11:00, 2nd floor of Carlson

### Prerequisites

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

### 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

You will find that the lectures and lectures 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
• lower bound = -infty
• upper bound = 1.96

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.

Here is a spreadsheet to estimate the volatility of a stock from historical price data:

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.

After the midterm, we will convert your raw midterm score to a curved midterm score between 0 and 100.

At the end of the course, we will convert your raw final exam score to a curved final exam score between 0 and 100. We will do the same with your raw average homework score.

Your final grade will be computed using curved scores in the formula above.

• 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 Wednesdays at the start of class.
• Homework assignments and due dates will be posted in the schedule below.
• No late submissions will be allowed.

### Final Exam

• Dec. 17, 4:00–7:00 PM, Goergen 101
• Duration: 3 hours
• Number of Questions: 9
• No notes, textbooks, calculators, phones, or other electronic devices.
• No make-up final exam with be given.
• Warning: The style of last year’s final exam questions may not be a perfect indicator of this year’s final exam questions, due to different professors between years.
• Last year’s final
• Solution to last year’s final
• Solutions to this year’s final

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 similiar 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

Office hours of all instructors and TAs are open to all MTH 210 students, regardless of which section they are registered for. 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.

### Schedule

This schedule is tentative. It may change according to our progress through the topics. Textbook and lecture notes reading is listed by section number.

Week of Aug 28
Topics: Basic probability
HW1 posted Wednesday night. HW1 Solution posted next Wednesday night.
No class on Monday.
Week of Sep 4
Topics: Basic probability, Arbitrage
Lecture Notes Reading: 1.3, 1.4, 2.1, 2.2, 2.3
HW1 due Wednesday. HW2 posted Wednesday night. HW2 Solution posted next Wednesday night.
No class on Monday.
Week of Sep 11
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
HW2 due Wednesday. HW3 posted Wednesday night. HW3 Solution posted next Wednesday night.
Week of Sep 18
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: 3.3, 3.4, 3.5, 3.6, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6
HW3 due Wednesday. HW4 posted Wednesday night. HW4 Solution posted next Wednesday night.
Week of Sep 25
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
HW4 due Wednesday. HW5 posted Wednesday night. HW5 Solution posted next Wednesday night.
Week of Oct 2
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
HW5 due Wednesday.
HW6 posted Wednesday night. HW6 Solution posted night of Wednesday, Oct 18.
HW7 posted early (content covered next week). HW7 Solution posted night of Wednesday night, Oct 18.
Week of Oct 9
Topics: Swap definition, Forward swap rate and swap value
Lecture Notes Reading: 6.1, 6.2, 6.3. 6.4
HW6 and HW7 due next Wednesday.
No class on Monday. No office hours this week.
Week of Oct 16
Topics: Spot-starting swaps, Swaps as difference between bonds, Physical versus cash settlement, Futures definition, Futures versus forward prices
Textbook Reading: 4.3, 4.4, 2.8, 5.1, 5.2
Lecture Notes Reading: 6.5, 6.6, 7.1, 7.2, 7.3, 7.4, 7.5
HW6 and HW7 due Wednesday. HW8 not posted; study for midterm instead.
Week of Oct 23
Topics: Option definitions, Put-call parity, Bounds on call prices
Lecture Notes Reading: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6
No HW due. HW8 posted Wednesday night. HW8 Solution posted next Wednesday night.
Midterm Exam: Thursday, October 26, 8:00-9:15 (AM), Dewey 1101
Week of Oct 30
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: 8.7, 8.8, 8.9, 8.10, 8.11, 8.12, 8.13
HW8 due Wednesday. HW9 posted Wednesday night. HW9 Solution posted next Wednesday night.
Week of Nov 6
Topics: Some advanced probability, Binomial Tree
Lecture Notes Reading: 9.1, 9.2, 9.3, 10.1, 10.2
HW9 due Wednesday. HW10 posted Wednesday night. HW10 Solution posted next Wednesday night.
Week of Nov 13
Topics: Binomial Tree, Fundamental Theorem of Asset Pricing
Textbook Reading: 8.1, 8.2, 8.3, 8.4
Lecture Notes Reading: 10.3, 10.2, 10.3, 10.4, 10.5
HW10 due Wednesday. HW11 posted Wednesday night. HW11 Solution posted next next Wednesday night.
Week of Nov 20
Topics: Binomial Tree, Fundamental Theorem of Asset Pricing
Textbook Reading: 8.1, 8.2, 8.3, 8.4
No class on Wednesday. No homework or office hours.
Week of Nov 27
Topics: Normal distribution and central limit theorem, Black-Scholes model