Topic for fall 2004: Introduction to mathematical finance.
Note: This course is offered in alternate years.
Instructor: Alan Durfee
Lectures: Monday, Wednesday, Friday 10:00-10:50 in Clapp 402.
Course Description: An introduction to mathematical finance. (An alternative title is "financial engineering".) Major topics covered: Mathematical model of stock prices (geometric Brownian motion), normality and independence of returns, mean-variance optimization, efficient frontier, capital asset pricing model, vanilla options (puts and calls), binomial trees, Black-Scholes formula as a limit of binomial trees, American and exotic options, Monte Carlo methods, bonds, models for interest rates.
There are master of finance programs at many universities. Here are a few (others can be found using Google):
In this course we will be learning the basics of material covered in more detail in such programs. Here are some words from the BU web site:
"Currently, sophisticated mathematical tools are used not only by traders of derivatives but also by any bank or corporation which has to determine how much to spend for development and research, the best time to enter/exit the market, or how much a particular acquisition is worth. This has forced essentially all major financial institutions in the U.S. to employ graduates with degrees in physics, engineering and mathematics."
The May 1998 issue of Scientific American has an article ("A calculus of risk") which is an introduction to the subject. It can be found online at http://www.sciam.com/1998/0598issue/0598stix.html.
Prerequsites: Mathematics 202 and at least one other course in mathematics or statistics at the two-hundred level or above, or permission of the instructor. The prerequisites for this course are rather minimal since we will develop most topics from scratch, including the necessary material from probability and statistics. However, as for any 300-level course, the more mathematics and/or statistics you know, the better off you will be.
Textbook: John C. Hull, Options, Futures, and Other Derivatives (5th ed), Prentice-Hall 2003. This is available at the Odyssey. The fourth edition is ok too. Recommended: The Wall Street Journal Guide to Understanding Money and Investing (the price is right).
The address of this page is www.mtholyoke.edu/courses/adurfee/f04/math339/math339-gen.htm. It also can be reached through my web page, the web page of the Department of Mathematics and Statistics, and the MHC course web page.
The address for the daily schedule is www.mtholyoke.edu/courses/adurfee/f04/math339/math339-sch.htm. The address for the syllabus is www.mtholyoke.edu/courses/adurfee/f04/math339/math339-syl.htm.