MIT-Topics in Mathematics with Applications in Finance

MIT-Topics in Mathematics with Applications in Finance

A flow diagram of a pricing model.

Description

The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. The course will consist of a set of mathematics lectures on topics in Linear Algebra, Probability, Statistics, Stochastic Processes and Numerical Methods. Mathematics lectures will be mixed with lectures illustrating the corresponding application in the financial industry.

MIT mathematicians will teach the mathematics part while industry professionals will give the lectures on applications in finance. We also plan to organize an optional field trip to visit Morgan Stanley offices in New York.

Goals for the Class

  1. Be able to derive price-yield relationship and understand convexity.
  2. Bootstrap a yield curve.
  3. Compute standard Value At Risk and understand assumptions behind it.
  4. Estimate volatility of an option.
  5. Derive Black-Scholes equations using risk-neutral arguments.
  6. Understand decomposition of matrices in statistics (and probability) point of view, e.g. principle component analysis.
  7. Use statistical techniques and methods in data analysis; understand the advantages and limitations of different methods.
  8. Understand basic limiting theorems and assumptions behind them.
  9. Understand Ito’s lemma and it’s applications in financial mathematics.
  10. Understand Girsanov’s theorem and change of measure.

Link: http://ocw.mit.edu/courses/mathematics/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/index.htm

Video Lectures

Lecture 1: Introduction, Financial Terms and Concepts

Lecture 2: Linear Algebra

Lecture 3: Probability Theory

Lecture 4: Matrix Primer

Lecture 5: Stochastic Processes I

Lecture 6: Regression Analysis

Lecture 7: Value At Risk (VAR) Models

Lecture 8: Time Series Analysis I

Lecture 9: Volatility Modeling

Lecture 10: Regularized Pricing and Risk Models

Lecture 11: Time Series Analysis II

Lecture 12: Time Series Analysis III

Lecture 13: Commodity Models

Lecture 14: Portfolio Theory

Lecture 15: Factor Modeling

Lecture 16: Portfolio Management

Lecture 17: Stochastic Processes II

Lecture 18: Itō Calculus

Lecture 19: Black-Scholes Formula, Risk-neutral Valuation

Lecture 20: Option Price and Probability Duality

Lecture 21: Stochastic Differential Equations

Lecture 22: Calculus of Variations and its Application in FX Execution

Lecture 23: Quanto Credit Hedging

Lecture 24: HJM Model for Interest Rates and Credit

Lecture 25: Ross Recovery Theorem

Lecture 26: Introduction to Counterparty Credit Risk

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