MATH 86: MATHEMATICAL FINANCE

Syllabus: Winter 2024 Instructors: Erik van Erp, John W. Welborn

Location: Rockefeller 003 Email: johannes.van.erp@dartmouth.edu

Tue/Thu: 2:25 – 4:15 PM Email: John.W.Welborn@dartmouth.edu

Wed X-Hour: 5:30 – 6:20 PM Office Hours: By Request

COURSE DESCRIPTION

Financial derivatives can be thought of as wagers on uncertain future financial events. This course will take a mathematically rigorous approach to understanding the Black-Scholes-Merton model and its applications to pricing financial derivatives and risk management. Topics will include arbitrage-free pricing, binomial tree models, measure theory, Ito calculus, the Black-Scholes analysis, derivatives pricing, the Greeks, and delta hedging.

PREREQUISITES

MATH 20 or MATH 60; and COSC 1 or ENGS 20 or equivalent

COURSE TEXTBOOKS

1. Baxter, Martin., and Andrew Rennie. Financial Calculus: An Introduction to Derivative Pricing. Cambridge: Cambridge University Press, 1996. Available online.

2. Wilmott, Paul. Paul Wilmott Introduces Quantitative Finance. 2nd ed. Chichester, West Sussex, England: J. Wiley & Sons Ltd., 2007. Available online.

GRADING:

• Problem Sets: 50% (Drop Lowest Grade)

• Final Exam: 30% (Start 3/5/24; Due 3/10/24 @ 600pm)

• Final Project: 20% (Due 3/8/24 @ 600pm)

EXAMS

The final exam (30%) will be open book and open note. Do your own work and adhere to the Academic Honor Principle. Students who require testing accommodations must contact us as soon as possible and provide the appropriate documentation.

FINAL PROJECT

Your final project (20%) may be on any topic related to mathematical finance. Students are encouraged to consider either an empirical or theoretical project. Potential topics include local volatility modeling, exotic options pricing formulae, numerical methods, and jump diffusion processes. Projects will be graded on novelty, quality, technical proficiency, and research. Final project groups may be up to 3-4 students in size, or you may work on your own.

PROBLEM SETS

There will be 4 problem sets due throughout the term. Each assignment is worth 5% of your final grade. For homework assignments, you may work in groups of no more than 2. To complete the assignment, upload a single, clear, and legible PDF and/or Jupyter notebook to Canvas.

ASSIGNMENT PREPARATION GROUPS

Students are expected to prepare problem set assignments and final projects in groups. If you do not wish to choose your own group, then you will be assigned to a group using Canvas’s random sorting algorithm. If your assigned group is not a good fit, or if you prefer to work on your own, then please contact the professors. Be respectful, responsive, and professional.

ACADEMIC HONOR PRINCIPLE

Fundamental to the principle of independent learning are the requirements of honesty and integrity in the performance of academic assignments, both in and out of the classroom. Dartmouth operates on the principle of academic honor, without proctoring of examinations. Any student who submits work which is not his or her own, or commits other acts of academic dishonesty, violates the purposes of the college and is subject to disciplinary actions, up to and including suspension or separation. All students must follow the Academic Honor Principle.

MENTAL HEALTH

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (http://www.dartmouth.edu/~upperde/), Counseling and Human Development (http://www.dartmouth.edu/~chd/), and the Student Wellness Center (http://www.dartmouth.edu/~healthed/).

STUDENT ACCESSIBILITY NEEDS

Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Apply for Services webpage; student.accessibility.services@dartmouth.edu; 1-603-646-9900) and to request that an accommodation email be sent to me in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with me to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the quarter as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.

RELIGIOUS OBSERVANCES

Dartmouth has a deep commitment to support students’ religious observances and diverse faith practices. Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me as soon as possible—before the end of the second week of the term at the latest—to discuss appropriate course adjustments.

COURSE OUTLINE