The purpose of the class is to expose students to the mathematical concepts and techniques used in the financial industry. Mathematics lectures are mixed with lectures illustrating the corresponding application in the real world. The topics are diverse. Single security analysis such as the pricing and hedging of derivative securities (e.g. options) involves the Ito Calculus and Stochastic Differential Equations. Portfolio level concerns include Mean Variance Optimization,  Value-at-Risk models and factor models (e.g. CAPM and APT). The study of volatility will bring in time series analysis. The course will consider a variety of asset classes including equity, debt and commodities. The course will be in English.

Syllabus

Linear Algebra

Probability Theory
Stochastic Processes
Regression Analysis
Value-at-Risk (VaR) Models
Time Series Analysis
Volatility Modeling
Portfolio Theory
Factor Modeling
Ito Calculus
Black-Sholes Formula, Risk-Neutral Valuation

Problem Sets, Exams and Grading

Approximately 9 problem sets will be assigned during the semester. If enrolment in the class is not too large the problem sets will be graded and will contribute substantially to the final grade. There will be a final take-home exam

Programming

Some of the programming examples in the lectures will involve the R programming language. Prior knowledge of R will be useful but is not required

Prerequisites

Single and multivariable calculus, probability and statistics, linear algebra. Differential equations would be helpful, as would some programming experience

[1] This course is modeled after a mathematics course offered at MIT: Topics in Mathematics with Applications in Finance. See https://ocw.mit.edu/courses/mathematics/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/index.htm

Related Literature

Hull, John. Options, Futures, and Other Derivatives. Prentice Hall (10th edition is 2017)

Baxter, Martin, and Andrew Rennie. Financial Calculus: An Introduction to Derivative Pricing. Cambridge University Press, 1996

Wilmott, Paul, Sam Howison, and Jeff Dewynne. The Mathematics of Financial Derivatives: A Student Introduction. Cambridge University Press, 1995

Grinold, Richard C., and Ronald N. Kahn. Active Portfolio Management: Quantitative Theory and Applications. Probus Pubulication Company, 1995

Fabozzi, Frank J., Sergio M. Focardi, and Petter N. Kolm. Financial Modeling of the Equity Market: From CAPM to Cointegration. Wiley, 2006

Tsay, Ruey S. Analysis of Financial Time Series. Wiley-Interscience, 2001