## 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

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:

Estimating Volatility Spreadsheet

### Grading

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.

Your letter grade will be determined by the following scale:

- 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.
- Your two lowest homework marks will be dropped when calculating your homework grade.

### Midterm Exam

- Date, Time, Location: Thursday, Oct. 26, 8:00–9:15 AM, Dewey 1101
- Duration: 75 minutes
- No notes, textbooks, calculators, phones, or other electronic devices.
- No accommodation for missing the midterm will be given.
- Covers up to and including Section 4.2 of the text.
- Last year’s midterm
- Solution to last year’s midterm
- This year’s midterm
- Solution to this year’s midterm

### 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.
- Bring your student ID.
- 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

### About The Exams

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.

### Academic Honesty

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.

### Additional Help

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
- Textbook Reading: None
- Lecture Notes Reading: 1.1, 1.2
- HW1 posted Wednesday night. HW1 Solution posted
**next**Wednesday night. - No class on Monday.
**Week of Sep 4**- Topics: Basic probability, Arbitrage
- Textbook Reading: 6.1
- 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
- Textbook Reading: 4.1, 4.2
- 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
- Textbook Reading: 7.1, 7.2, 7.3
- 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
- Textbook Reading: 9.5
- 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
- Lecture Notes Reading: 10.6, 10.7
- No class on Wednesday. No homework or office hours.
**Week of Nov 27**- Topics: Normal distribution and central limit theorem, Black-Scholes model
- Textbook Reading: 10.1, 10.2, 10.3
- Lecture Notes Reading: 12.1, 12.2, 12.3, 13.1, 13.2, 13.3
- HW11 due Wednesday. HW12 posted Wednesday night. HW12 Solution posted
**next**Wednesday night. **Week of Dec 4**- Topics: Properties of Black-Scholes model, Delta and vega, Volatility
- Textbook Reading: 10.4, 10.5
- Lecture Notes Reading: 13.4, 13.5, 13.6
- HW12 due Wednesday. HW13 posted Wednesday night. HW13 Solution posted
**this**Wednesday night. - HW13 is not to be handed in, but the material may appear on the final exam.
**Week of Dec 11**- Topics: Review
- No class on Wednesday or Friday.
- Final Exam: Sunday, Dec. 17, 4:00–7:00 PM, Goergen 101