Topic for spring 2007: 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: The basics of probability and statistics, risk-free investments (money in the bank), mathematical model of stock prices (geometric Brownian motion), normality and independence of returns, mean-variance optimization, efficient frontier, capital asset pricing model (the latter three time permitting), 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.
"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." (from the BU web site below)
There are master of finance programs at many universities; a few are listed below. In this course we will be learning the basics of material covered in more detail in such programs.
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 (6th ed), Prentice-Hall 2006. This is available at the Odyssey. The fifth and fourth editions are ok too. Recommended: Standard and Poor's Guide to Money and Investing (available at the Odyssey--the price is right). Handouts can be picked up from the envelope on my bulletin board.
Homework: There will be regular homework assignments. Homework can be handed in during class or put in the envelope outside my office door. Please turn in homework on time! Graded homework can be picked up any time from the other envelope there. Homework can be redone and handed in again.
Tests and Quizzes:There will be two take-home open-book tests and a final examination (also open book take home). There will be quizzes in class. These will be announced in advance. If you are unable to take a test or quiz for any reason, you should let me beforehand. (You may call my answering machine at x2299 at any time, day or night.) They can always be taken early.
Grading: Roughly: Homework is 40%, the tests and final are 35%, and quizzes are 25%.
Books on reserve: