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18.642 | Fall 2024 | Undergraduate

# Topics in Mathematics with Applications in Finance

Note: Every group member should submit a different 5–7 page draft focusing on their particular section.

Prepare an introductory, written lecture note on the topic with the target audience being fellow students with no prior knowledge of the topic.

#### Draft 1 Assignment

Your objectives in this assignment are to demonstrate active individual work on the group project and to solicit feedback on your progress thus far. Depending on your topic, your draft may include 3-4 polished pages of content plus 1-2 pages of introduction/motivation, or it might include 5-7 pages of notes discussing/developing mathematical content. It can be anywhere in between these two descriptors, or you can aim for a more complete draft than 3-4 pages. While you may be working in a group, submissions for this assignment should be by individual, focusing on your contribution/section-responsibilities in the final paper. The final section of your submission should be a reflection section in which you identify what feedback you would like to receive—that is, what questions you have for how to proceed with the project presentation and lecture note.

#### Assessment

Your grade on this draft will be based on evidence of individual focused, productive effort on the group project (as evidenced by 5+ pages of draft text and/or content).

#### Project Timeline

In the week after, you will be asked to peer review another group’s draft notes and continue revising the note and preparing the oral presentation. Oral presentations (15–20 minutes) of lecture notes will be scheduled in class subsequently.

#### Group Project Topics

- How Human Fallacies Lead to Market Anomalies
- Regression Modeling of UK Property Prices
- The Use of Machine Learning in Predicting Future Interest Rates
- Alternative Data
- Jump-Diffusion Model
- Maximizing Utility While Minimizing Risk
- Fourier Analysis and Its Applications in the Stock Market
- Black Scholes Merton Model
- Implied Volatility
- Partial Differential Equation Models for Option Pricing
- Manipulating the Sports Betting Market
- Time Series Modeling
- Analyzing Volatility Curves in Option Pricing
- The Black-Scholes Model
- Delta-Hedging—The Basics of Options Trading Strategies

## Course Info

##### Instructors

- Dr. Peter Kempthorne
- Dr. Vasily Strela
- Dr. Jake Xia

##### Departments

- Mathematics

##### As Taught In

Fall 2024

##### Level

Undergraduate

##### Topics

- Business
  - Finance
- Mathematics
  - Applied Mathematics
  - Probability and Statistics

##### Learning Resource Types

notes Lecture Notes
theaters Lecture Videos
assignment Problem Sets
assignment Activity Assignments
group_work Projects
Readings

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