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
- Be able to derive price-yield relationship and understand convexity.
- Bootstrap a yield curve.
- Compute standard Value At Risk and understand assumptions behind it.
- Estimate volatility of an option.
- Derive Black-Scholes equations using risk-neutral arguments.
- Understand decomposition of matrices in statistics (and probability) point of view, e.g. principle component analysis.
- Use statistical techniques and methods in data analysis; understand the advantages and limitations of different methods.
- Understand basic limiting theorems and assumptions behind them.
- Understand Ito’s lemma and it’s applications in financial mathematics.
- Understand Girsanov’s theorem and change of measure.
Lecture 4: Matrix Primer
Lecture 22: Calculus of Variations and its Application in FX Execution
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