## Math 210 - Introduction to Financial Mathematics

### Instructors

- Kyle Hambrook
- Lectures: MWF 10:25-11:15 GAVET 310
- E-mail: kyle dot hambrook at rochester dot edu
- Office: Hylan 905
- Help Hours: MW 17:00-18:00
- Jie Zhong
- Lectures: MW 12:30-13:45 MOREY 321
- E-mail: jie dot zhong at rochester dot edu
- Office: Hylan 1008
- Help Hours: MWF 10:00-11:00

### TAs

- Junting Zhou
- E-mail: jzhou40 at u dot rochester dot edu
- Help Hours: Monday, 6:20PM-7:20PM, Carlson Library, 2nd Floor.
- Chengyu Deng
- E-mail: cdeng2 at u dot rochester dot edu
- Help Hours: Monday, 2:00PM-3:00PM, Carlson Library, 1st Floor.
- Yifan Ni
- E-mail: yni10 at u dot rochester dot edu
- Help Hours: Tuesday, 3:00PM-4:00PM, Carlson Library, 2nd Floor.
- Xingyu Zhu
- E-mail: xzhu8 at u dot rochester dot edu
- Help Hours: Friday, 1:00PM-2:00PM Carlson Library, 1st Floor.

### Prerequisites

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.

### Lecture Notes, Slides, and Other Resources

Lectures will be based on the lecture notes, but will not be identical to the them. The lecture notes will have additional examples, exercises, and comments. The lecture notes will be updated over time.

Here is a supplement to the lecture notes:

Supplement - Interest Rates, Forward Rates, and Forward Rate Agreements

The slides are based on the lectures notes. The slides will be updated over time.

Here is a table to find values of Phi, the 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 values of Phi, the 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 is a spreadsheet to estimate the volatility of a stock from historical price data:

Estimating Volatility Spreadsheet

### Main Textbook

*An Introduction to Quantitative Finance* by Stephen Blyth

### Supplementary Textbooks

*Mathematics for Finance: An Introduction to Financial Engineering* by Marek Capinski and Tomasz Zastawniak

*An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation* by Desmond Higham

### About the Textbooks

You are strongly recommended to obtain the main textbook and the first supplementary textbook.

We will mostly follow the notation and order of presentation of the main textbook. You may find that the main textbook has too few examples.

We will be discussing many examples in lectures, but you will likely find it useful to have the first supplementary textbook as another source of examples.

The first supplementary textbook was used in this course last year.

You may find the alternate presentation of the second optional textbook useful.

### Grading

- Homework: 20%
- Midterm Exam: 30%
- Final Exam: 50%
- If it results in a higher course grade for you, your midterm will be worth 0% and your final exam will be worth 80%.

### 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

- Thursday, October 27, 8:00-9:30 AM, HUTCH 141
- 6 questions, 75 minutes
- It will cover all material BEFORE futures contracts.
- You are allowed one sheet of notes (front and back, standard letter size paper).
- You are allowed a non-programmable, non-graphing calculator.
- No other notes, textbooks, phones, or other electronic devices.
- No accommodation for missing the midterm will be given.
- The exam questions will be:
- Definition statements from class
- Result statements from class
- Proofs from class
- Examples from class (possibly with small variations)
- Exercises from homework (possibly with small variations)

- Study these things to do well on the exam.
- Midterm and Midterm - solutions
- Midterm scores are posted on Blackboard. It is a score out of 17.
- Here is a rough approximation of the letter grade corresponding to your midterm score. “B” means “B- or B or B+”, etc.
- A: 13-17
- B: 9-12
- C: 6-8
- D: 4-5
- F: 0-3

### Final Exam

- Saturday, December 17, 16:00
- Location: Hambrook - Meliora Hall 203, Zhong - Dewey 1101
- No make-up final with be given
- Bring your student ID.
- You are allowed a calculator. It cannot have the ability to transmit or receive messages.
- You are allowed one sheet of notes.
**One side**,**hand-written**,**standard letter-size paper**. - The final exam will also include a formula sheet and a table of values for Phi. The same formula sheet and table of values is included in the practice final below.
- The exam questions will be:
- Definition statements from class
- Result statements from class
- Proofs from class
- Examples from class (possibly with small variations)
- Exercises from homework (possibly with small variations)

- Study these things to do well on the exam.
- Practice Final Exam. The final exam will have a very similar format, including the same formula sheet and table of values for Phi.
- Practice Final Exam “Solutions”
- The “solutions” are mostly directions to where in the Lecture Notes or HW exercises the solution can be found. I will improve the solutions a bit on Wednesday, Dec 14.
- Final Exam Solutions - Hide Until After Dec 17
- Final Exam Solutions - Seriously This Time

### 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

If you are having any difficulties, seek help immediately - do not wait until it is too late to recover from falling behind or failing to understand a concept. Ask an instructor or TA either in class, during office hours, or during an appointment. Email your instructor or TA, or use the WebWork “email WeBWorK TA” button. Work with your classmates (this is always a good idea). It is essential not to fall behind because each lecture is based on previous work.

### Disability Resources

If you have an academic need related to a disability, contact the Center for Excellence in Teaching and Learning (CETL).

The University of Rochester is committed to providing equal educational opportunities for individuals with disabilities. Costs of required auxiliary services are to be borne by the university, not by the student. For more complete information about disabilities, please read the disability handbook which is available on the CETL page.

To be granted alternate testing accommodations, you (the student) must fill out forms with CETL 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 CETL, and they are not obligated to make any accommodations on their own.

### Schedule

This schedule is tentative. It may change according our progress through the topics. Section numbers are for the textbook *An Introduction to Quantitative Finance* by Stephen Blyth.

- Week of Aug 29
- Topics: Review of basic probability
- HW1 posted.
- No class on Monday.
- Week of Sep 5
- Topics: Review of probability, Arbitrage
- Textbook Reading: 6.1
- HW2 posted. HW1 due Wednesday. HW1 Solution.
- No class on Monday.
- Week of Sep 12
- Topics: Monotonicity and replication, Interest rates and compounding, Zero coupon bonds and discounting,
- Textbook Reading: 6.2, 1.1, 1.2, 1.3
- HW3 posted. HW2 due Wednesday. HW2 Solution.
- Week of Sep 19
- 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
- HW4 posted. HW3 due Wednesday. HW3 Solution.
- Week of Sep 26
- 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
- HW5 posted. HW4 due Wednesday. HW4 Solution.
- Week of Oct 3
- 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
- HW6 posted. HW5 due Wednesday. HW5 Solution.
- Week of Oct 10
- 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
- HW7 posted. HW6 due Wednesday. HW6 Solution.
- Week of Oct 17
- Topics: Futures definition, Futures versus forward prices
- Textbook Reading: 5.1, 5.2
- HW7 due Wednesday. HW7 Solution.
- No class on Monday.
- Week of Oct 24
- Topics: Option definitions, Put-call parity, Bounds on call prices
- Textbook Reading: 7.1, 7.2, 7.3
- HW8 posted.
- Midterm Exam. Thursday, October 27, 8:00-9:30 (AM), HUTCH 141
- Week of Oct 31
- Topics: Call and put spreads, Call butterflies, Digital options
- Textbook Reading: 7.4, 7.5, 7.6
- HW9 posted. HW8 due Wednesday. HW8 Solution.
- Week of Nov 7
- Topics: Review of conditional probability, Fundamental Theorem of Asset Pricing
- Textbook Reading: 9.5
- HW10 posted. HW9 due Wednesday. HW9 Solution
- Week of Nov 14
- Topics: Binomial Tree
- Textbook Reading: 8.1, 8.2, 8.3, 8.4
- HW11 posted on
**Friday**. HW10 due Wednesday. HW10 Solution - Week of Nov 21
- No class on Monday, Wednesday, or Friday. No homework or office hours.
- Week of Nov 28
- Topics: Review of normal distribution and central limit theorem, Lognormal limit, Risk-neutral limit, Black-Scholes Formula
- Textbook Reading: 10.1, 10.2, 10.3
- HW12 posted. HW11 due Wednesday. HW11 Solution
- Week of Dec 5
- Topics: Properties of Black-Scholes formula, Delta and vega
- Textbook Reading: 10.4, 10.5
- HW13 posted. HW12 due Wednesday. HW12 Solution and HW13 Solution <– Done
- HW13 is not to be handed in, but the material may appear on the final exam.
- Week of Dec 12
- Review
- No class on Wednesday or Friday.
- Final Exam. Saturday, December 17, 16:00-19:00. Hambrook - Meliora Hall 203. Zhong - Dewey 1101.