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MATH 5870/6870: Financial Mathematics

2021 Fall, Auburn University

Contact

Instructor Dr. Le Chen
Email le.chen@auburn.edu
Class Time MWF, 10:00 -- 10:50
Class Room PARKR 228
Office hours MW, 13:00 -- 14:00, or via appointment/Zoom upon request

Course description

The course serves as an introduction to mathematical aspects of pricing of financial derivatives including the Black-Scholes model and the binomial option pricing model. Topics also include partial differential equations and relevant numerical methods.

Textbook

The following two books will be the main references for this course:

Coverage

The course will cover the following topics

The course is designed for the first time by the instructor. The content of the subject is huge and we can only try to cover a subset of the content of the book -- Derivatives Markets. We have selected 13 chapters as listed below in the slides session, among which we will make some further selections of topics from these 13 Chapters throughout the semester.

Prerequisite

Students obligations

In order to successfully master the material and complete the course, you are expected to

Note: The syllabus was created in March 2021, and it is subject to changes during the semester.

Assignments

Attendance

Assessment

Slides

Chapter/Section Slides Slides
Chapter 1: Introduction to Derivatives presentation compact
1.1. What is a derivative? pres. comp.
1.2. The role of financial markets pres. comp.
1.3. The use of derivatives pres. comp.
1.4. Buying and short-selling financial assets pres. comp.
1.5. Problems pres. comp.
Chapter 2: An Introduction to Forwards and Options presentation compact
2.1. Forward contracts pres. comp.
2.2. Call options pres. comp.
2.3. Put options pres. comp.
2.4. Summary of forward and option positions pres. comp.
2.5. Problems pres. comp.
Chapter 3: Insurance, Collars, and Other Strategies presentation compact
3.1. Basic insurance strategies pres. comp.
3.2. Put-call parity pres. comp.
3.3. Spreads and collars pres. comp.
3.4. Speculating on volatility pres. comp.
3.5. Problems pres. comp.
Chapter 5: Financial Forwards and Futures presentation compact
5.1. Alternative ways to buy a stock pres. comp.
5.2. Prepaid forward contracts on stock pres. comp.
5.3. Forward contracts on stock pres. comp.
5.4. Futures contracts pres. comp.
5.5. Problems pres. comp.
Chapter 9: Parity and other option relationships presentation compact
9.1. Put-call parity pres. comp.
9.2. Generalized parity and exchange options pres. comp.
9.3. Comparing options with respect to style, maturity, and strike pres. comp.
9.4. Problems pres. comp.
Chapter 10: Binomial Option Pricing: Basic Concepts presentation compact
10.1. A one-period Binomial tree pres. comp.
10.2. Constructing a Binomial tree pres. comp.
10.3. Two or more binomial periods pres. comp.
10.4. Put options pres. comp.
10.5. American options pres. comp.
10.6. Options on other assets pres. comp.
10.7. Problems pres. comp.
Chapter 11: Binomial Option Pricing: Selected Topics presentation compact
11.1. Understanding Early Exercise pres. comp.
11.2. Understanding risk-neutral pricing pres. comp.
11.3. The Binomial tree and lognormality pres. comp.
11.4. Problems pres. comp.
Chapter 12: The Black-Scholes Formula presentation compact
12.1. Introduction to the Black-Scholes formula pres. comp.
12.2. Applying the formula to other assets pres. comp.
12.3. Option Greeks pres. comp.
12.4. A. The standard normal distribution pres. comp.
12.5. B. Formulas for option Greeks pres. comp.
12.6. Problems pres. comp.
Chapter 13: Market-Making and Delta-Hedging presentation compact
13.1. What do market-makers do? pres. comp.
13.2. Market-maker risk pres. comp.
13.3. Delta-Hedging pres. comp.
13.4. The mathematics of Delta-hedging pres. comp.
13.5. The Black-Scholes analysis pres. comp.
13.6. Market-Making as insurance pres. comp.
13.7. Problems pres. comp.
Chapter 14: Exotic Options: I presentation compact
14.1. Introduction pres. comp.
14.2. Asian options pres. comp.
14.3. Barrier options pres. comp.
14.4. Compound options pres. comp.
14.5. Gap options pres. comp.
14.6. Exchange options pres. comp.
14.7. Problems pres. comp.
Chapter 18: The Lognormal Distribution presentation compact
18.1. The normal distribution pres. comp.
18.2. The lognormal distribution pres. comp.
18.3. A lognormal model of stock prices pres. comp.
18.4. Lognormal probability calculations pres. comp.
18.5. A. The expectation of a lognormal variable pres. comp.
18.6. B. Constructing a normal probability pres. comp.
18.7. Problems pres. comp.
Chapter 19: Monte Carlo Valuation presentation compact
19.1. Computing the option price as a discounted expected value pres. comp.
19.2. Computing random numbers pres. comp.
19.3. Simulating lognormal stock prices pres. comp.
19.4. Monte Carlo valuation pres. comp.
19.5. Efficient Monte Carlo valuation pres. comp.
19.6. Valuation of American options pres. comp.
19.7. The Poisson distribution pres. comp.
19.8. Simulating jumps with the Poisson distribution pres. comp.
19.9. Simulating correlated stock prices pres. comp.
19.10. Problems pres. comp.
Chapter 20: Brownian Motion and Ito Lemma presentation compact
20.1. The Black-Scholes assumption about stock prices pres. comp.
20.2. Brownian motion pres. comp.
20.3. Geometric Brownian motion pres. comp.
20.4. The Ito formula pres. comp.
20.5. The Sharpe ratio pres. comp.
20.6. Risk-neutral valuation pres. comp.
20.7. Problems pres. comp.

Tentative schedule

Face Covering Policy

We will follow the university policy regarding face covering: 

Students enrolled in this course are required to wear a face covering that covers the nose and mouth
while inside the classroom, laboratory, faculty member offices, or group instructional spaces.
Failure to comply with this requirement represents a potential violation of Code of Student Conduct
and may be reported as a non-academic violation.

Please consult the Auburn University Classroom Behavior Policy at

for additional details.

Honor code

Accessibility

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility to determine how you could improve your learning as well. You can register and make a request for services from the Office of Accessibility. In this case, please do inform me of such requests. See the following link for more information:

Harassment and Discrimination


Auburn University is committed to providing a working and academic environment free from prohibited
discrimination and harassment and to fostering a nurturing and vibrant community founded upon the
fundamental dignity and worth of all its members. Auburn University prohibits harassment of its
students and employees based on protected classes and works to eliminate prohibited behavior from
its academics and employment through corrective measures and education.

The Office of AA/EEO oversees compliance with the Policy Prohibiting Harassment of Students, the
Policy Prohibiting Harassment of Employees, and the Policy on Sexual and Gender-Based Harassment and
Other Forms of Interpersonal Violence.

Protected classes are race, color, sex (which includes sexual orientation, gender identity, and
gender expression), religion, national origin, age, disability, protected veteran status, or genetic
information.

Auburn University also prohibits retaliation against any individual for opposing a practice he/she
reasonably believed to be discriminatory; for filing an internal or external complaint, grievance,
or charge; or for participating in any investigation or proceeding, in accordance with Auburn
University's policies.

Acknowledgement

© Le Chen, Auburn, 2021.