MATH 96: MATHEMATICAL FINANCE II

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

Location: Haldeman 046 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

This course is a continuation of MATH 86 with an emphasis on the mathematics underlying fixed income derivatives. Topics may include exotic derivative pricing, stochastic calculus, Radon-Nikodym derivative and change of measure, Girsanov's theorem, the Martingale representation theorem, interest rate models (e.g., H-J-M, Ho-Lee, Vasicek, C-I-R), interest rate derivatives, interest rate trees and model calibration, and credit derivatives.

PREREQUISITES

• MATH 86, and MATH 23

COURSE TEXTBOOKS

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

2. Derman, E., & Miller, M. B. 2016. The Volatility Smile. Wiley. Available online.

3. Gatheral, J. 2006. The Volatility Surface: A Practitioner’s Guide. John Wiley & Sons. Available online.

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

5. Wilmott, Paul. 2006. Paul Wilmott on quantitative finance (2nd ed.). John Wiley & Sons. Available online.

6. Wilmott, P., Howison, S., & Dewynne, J. 1995. The mathematics of financial derivatives: a student introduction. Cambridge University Press. Available online.

GRADING:

• Problem Sets: 50%

• Final Exam: 30%

• Final Project: 20%

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%) should connect to a topic covered in Math 96: Mathematical Finance II. 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 2 students in size, or you may work on your own.

PROBLEM SETS

There will be weekly problem sets due throughout the term worth a total of 50% of your 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 Jupyter notebook (as needed) 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