Topic for fall 2008: 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: Risk-free investments (money in the bank) and interest rates, a mathematical model of stock prices (geometric Brownian motion), the basics of probability and statistics, normality and independence of returns, forwards, futures, basic options and their uses (puts and calls), binomial trees, Black-Scholes formula as a limit of binomial trees, the Black-Scholes PDE via stochastic differential equations, implied volatility and volatility smiles, American and exotic options, the Greeks, and Monte Carlo methods.
"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 203 and 211, or permission of the instructor. The actual 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. Earlier editions are also ok. 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.
TA: Pratistha Joshi (email: joshi20p@mtholyoke.edu). She will be grading some of the homework assignments, and is also willing to meet with people to discuss the homework.
Tests and Quizzes:There will be three take-home open-book tests. The first will be handed out Wednesday 10/29 at the end of class, and is due at the beginning of class Monday 10/27. The second will be handed out on Wednesday 11/12 and will be due Monday 11/17. The third will be handed out on the last day of classes and will be due at the end of exam period. 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 (Email me, or call my office phone/answering machine anytime day or night.) They can always be taken early.
Grading: Roughly: Homework is 40%, the tests are 45%, and quizzes are 15%.
Books on reserve: