Topics in Mathematics with Applications in Finance
This is the first version of {{% resource_link "d1090ad2-6097-4c81-b758-c21d1243282b" "*18.642 Topics in Mathematics with Applications in Finance*" %}} from Fall 2024. Please visit the {{% resource_link "d1090ad2-6097-4c81-b758-c21d1243282b" "*18.642* site" %}} for more materials and lecture recordings. {{% resource_link "b499266c-7576-4867-bdae-c241c9a8b096" "An investment game" %}} is also available as an additional learning resource. The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. Mathematics lectures are mixed with lectures illustrating the corresponding application in the financial industry. MIT mathematicians teach the mathematics part while industry professionals give the lectures on applications in finance.
Syllabus
- 1 Lecture 1: Introduction, Financial Terms and Concepts
- 2 Lecture 2: Linear Algebra
- 3 Lecture 3: Probability Theory
- 4 Lecture 5: Stochastic Processes I
- 5 Lecture 6: Regression Analysis
- 6 Lecture 7: Value At Risk (VAR) Models
- 7 Lecture 8: Time Series Analysis I
- 8 Lecture 9: Volatility Modeling
- 9 Lecture 10: Regularized Pricing and Risk Models
- 10 Lecture 11: Time Series Analysis II
- 11 Lecture 12: Time Series Analysis III
- 12 Lecture 13: Commodity Models
- 13 Lecture 14: Portfolio Theory
- 14 Lecture 15: Factor Modeling
- 15 Lecture 16: Portfolio Management
- 16 Lecture 17: Stochastic Processes II
- 17 Lecture 18: Itō Calculus
- 18 Lecture 19: Black-Scholes Formula, Risk-neutral Valuation
- 19 Lecture 20: Option Price and Probability Duality
- 20 Lecture 21: Stochastic Differential Equations
- 21 Lecture 23: Quanto Credit Hedging
- 22 Lecture 24: HJM Model for Interest Rates and Credit
- 23 Lecture 25: Ross Recovery Theorem
- 24 Lecture 26: Introduction to Counterparty Credit Risk
Course materials
- Course on MIT OpenCourseWare ↗ website