MATH 570: Quantitative Finance I (S26)
Turning Financial Theory into Computational Reality. As the foundational course in the Quantitative Data Science sequence, MATH 570 builds the rigorous mathematical, probabilistic, and statistical frameworks necessary for modern Quantitative Finance. We move beyond abstract theory to equip you with the tools needed for real-world financial modeling and data-driven decision-making.
Course Information
- Instructor: Shen-Ning Tung (tung@math.nthu.edu.tw)
- Lecture Time: Wednesdays, 14:20 PM – 15:10 PM and Fridays, 10:10 AM - 12:00 AM
- Office Hours: By appointment
- Target Audience: Upper-level Undergraduate and Graduate students in Quantitative Finance, Mathematics, and Data Science.
Course Description
Students will explore the core concepts of probabilistic modeling (including conditional independence and copulas) and mean-covariance statistics. The course bridges theory and practice through a balanced curriculum:
- Theory (40%): Lectures focusing on mathematical intuition, rigorous concepts, and derivations.
- Context (20%): Analysis of real-world financial problems and influential academic papers.
- Implementation (40%): Hands-on coding assignments utilizing Python for sophisticated data analysis.
Learning Objectives
By the end of this course, students will be able to:
- Apply suitable data-driven models to interpret and explain complex financial datasets.
- Analyze large-scale financial data using Python (NumPy/Pandas) to derive actionable quantitative insights.
- Evaluate academic financial literature and replicate theoretical models through rigorous computational implementation.
- Communicate technical findings and methodology effectively using Markdown and Jupyter Notebooks.
Prerequisites
- Mathematics: Strong proficiency in Multivariate Calculus, Linear Algebra, and Probability Theory.
- Programming: Basic proficiency in Python (specifically NumPy and Pandas).
Evaluation & Projects
- Coding Assignments (50%): Biweekly problem sets requiring the application of mathematical concepts through Python-based simulations and analysis.
- Final Project (50%): A substantial independent or group project. You will demonstrate mastery of a core course concept by analyzing a financial dataset of your choice, presented through professional data visualizations and quantitative metrics.
Project Milestone: Finalize your teammates and discuss your topic with the instructor by the end of March.
Logistics & AI Policy
- Communication: All announcements are made via the course Discord. Please use public channels for material-related questions to foster collaborative learning.
- Submissions: All work (notes and reports) must be submitted as Markdown or Jupyter Notebooks.
- AI Usage: Unrestricted use of AI tools (e.g., ChatGPT, Claude) is permitted for all assignments. No formal disclosure or citation is required. However, students remain 100% responsible for the accuracy, logic, and originality of their final submissions.
Course Schedule
| Week | Topic | Key Concepts |
|---|---|---|
| 1 | Introduction | Overview of QF & Financial Data Science |
| 2 | Probabilistic Framework-1 | Distributions, Transformations, and Elicitability |
| 3 | Probabilistic Framework-2 | Independence, Conditioning, and Copulas |
| 4 | Mean-Covariance Framework-1 | Mean, Covariance, and Affine Transformations |
| 5 | Mean-Covariance Frameworkt-2 | Uncorrelation, Linear Projection, and Connections with Conditional Independence |
| 6 | Estimation-1 | Statistical Decision Theory |
| 7 | Estimation-2 | Estimation Theory |
| 8 | Estimation-3 | Model Selection |
| 9 | Inference | Views, Black-Litterman |
| 10 | Linear Mean-Covariance Statistics-1 | Foundations, Linear Regression |
| 11 | Linear Mean-Covariance Statistics-2 | Principal Component Analysis |
| 12 | Linear Mean-Covariance Statistics-3 | Factor Analysis, Linear Optimal Transport |
Resources
- Primary: Instructor-provided Course Notes.