21-270 Introduction to Mathematical Finance

Description

This course is an introduction to the mathematical modeling of financial markets with particular emphasis on pricing derivative securities and management of risk.

Topics covered will include: an introduction to financial instruments and markets; the fundamental concepts of arbitrage, replication and completeness; cash flows and rates of return; simple models for random variation in prices; utility functions, mean-variance analysis; and the use of arbitrage free models for valuation of securities and for risk management.

The course will focus on the understanding of fundamental concepts rather than on memorizing recipes for specific situations. Although there are no prerequisites beyond knowledge of high school mathematics and elementary calculus, some of the concepts contained in the course are rather deep. Students will be asked to solve new and unfamiliar types of mathematical finance problems by utilizing the basic principles presented in the course.

Learning Objectives

After completing this course, you should be able to

1. Understand the similarities and differences among the main asset classes: equities, fixed income securities, and commodities.
2. Internalize the concept of pricing by replication. Use pricing by replication to detrmine the value of forward contracts, stock options, and fixed income securities.
3. Develop short but rigorous proofs of true mathematical statements about financial models. Construct counter-examples for false statements.
4. Understand risk neutral probability measures and the fundamental theorems of asset pricing.

How to use this site...

Home

The description gives a brief overview of the topics we will discuss this semester. The learning objectives give an itemized list of the skills you should be developing. The list of learning objectives may give you some useful direction in terms of studying for exams.

Course Information

Times and rooms for lecture and recitation sections.

Canvas

Course materials will be distributed through Canvas, and assignment grades will be recorded in the Canvas gradebook.

Schedule

List of topics to be covered each week, with links to reading assignments and homework.

Policies

Information about the calculation of grades, dates for exams, policies for late assignments and other matters. Familiarize yourself with these policies early in the semester.