GIVE NOW about ocw help & faqs contact us
18.642 | Fall 2024 | Undergraduate

# Topics in Mathematics with Applications in Finance

#### Final Paper Proposal

The final paper proposal should include the following:
* Final paper topic or tentative paper title
* Objective of the paper
* List of resources you plan to use (e.g., specific articles, web sites, as appropriate)

Every student will write their own final paper. It is fine to propose a continuation or extension of the group project topic, but each paper (or specific sections of a group project paper) will be an individual effort.

Final papers are due the last day of lectures. The paper grade will be based in part on math content, quality of writing, and logical flow/organization. It can be a group project but with clearly named individual sections. The grade is individual! Papers will have typical lengths of 10–15 pages.

#### Final Paper Draft 1 Notes

##### Description:

Your objectives in this assignment are to demonstrate active work on the final paper and to solicit feedback on your progress thus far. Depending on your our 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.

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 research and writing.

##### Assessment

Your grade on this draft will be based on evidence of focused, productive report in the research and writing of your paper (as evidenced by 5+ pages of draft text and/or content)

This assignment will include peer reviews in the following week.

#### Final Paper List of Topics

- The Effect of Credit Expansion on Land Prices
- Effects of Presidential Elections on Market Volatility
- Quantitative Methods in Sports Betting: Relative Value Binary Options
- Stochastic Volatility Modeling Using SABR
- A Comparative Analysis of Option Pricing Approaches and Practical Trading Strategies
- Portfolio Investments for NASA Technology Projects
- Methods of Portfolio Weight Allocation: From Mean-Variance Optimization to Black-Litterman Model
- Game Theory in Financial Markets
- Jiang Markov Chains and Gambler’s Ruin
- Stochastic Volatility Models: From Black-Scholes to Heston to SABR Models
- Volatility Forecasting with Volatility Surface
- Advancements in Pricing and Trading Strategies Using Artificial Intelligence
- Momentum Effects in Equity Markets: An Empirical Analysis from Monthly to Intra-Day Frequencies
- Interest Rate Modeling
- Assessing the Performance and Volatility of DEI-focused ETFs: A Comparative Analysis Against Index Funds
- Mathematical Foundations of Pairs Trading
- Predicting Daily Volume of S&P 500 stocks
- Exploring Different Analytical Call Option Pricing Methods for Black-Scholes Model and Jump Diffusion Model
- Cryptocurrency Volatility and Price Dynamics: A Probabilistic Modeling Approach
- A Comparative Study of Black-Scholes and Monte Carlo Methods for Option Pricing
- Predicting Volatility in Options Markets Using LSTM Networks
- How Do Insurance Companies Make Money?
- The Linear Algebra of Principal Component Analysis and its Applications in Finance
- Monte Carlo Simulation for Pricing Simple Options under Black-Scholes Dynamics and Jump-Diffusion Process
- The Forex Market
- Martingale Theory in Gambling: Returns and Paradoxes
- The Wolf of Wall Street: The Impact of Cinematography on the Stock Market
- The Greeks: Derivations and Implications in Risk Management and Trading
- Extreme Risk in Financial Markets: Modeling Tail Dependencies and Hedging Solutions
- The Pandemic’s Impact on the Housing Market in New York Counties
- Estimating Asset Probability Distributions Using Market Data
- Reinforcement Learning Techniques for Gamma and Vega Hedging
- Volume Prediction
- Sentiments and Option Pricing

## 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

Browse Resources

# You are leaving MIT OpenCourseWare

Please be advised that external sites may have terms and conditions, including license rights, that differ from ours. MIT OCW is not responsible for any content on third party sites, nor does a link suggest an endorsement of those sites and/or their content.