Topic for fall 2001: Introduction to mathematical finance.
Instructor: Alan Durfee
Lectures: Monday, Wednesday, Friday 11:00-11:50 in Clapp 401.
Course Description: The course in the fall of 2001 will be an introduction to mathematical finance. Topics to be selected from: interest rates, present and future value, stocks, options, the geometric Brownian motion model of stock prices, arbitrage pricing, binomial trees, stochastic calculus, the Black-Scholes equation, the Greeks, valuation by expected utility, exotic options, alternative to Black-Scholes, interest rate derivatives, Monte Carlo simulation, and statistical analysis of financial data.
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.
Textbook: John C. Hull, Options, Futures, and Other Derivatives (4th ed), Prentice-Hall 2000.
Some more details: The prerequisites for this courses are rather minimal since we will develop topics from scratch. However, as for any 300-level course, the more mathematics you know, the better off you will be. A course in statistics is also good background to have.
Several institutions now have MFA programs in mathematical finance, including Boston University, New York University, Columbia University and Stanford University. Here are some words from the web site for the BU program:
"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."
In this course we will be learning some of these sophisticated mathematical tools.
(Students who have taken Math 339 in the spring of 2000 may take it again.)
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.
The address of this page is www.mtholyoke.edu/courses/adurfee/f01/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/f01/math339/math339-sch.htm.