Math 339: Topics in Applied Mathematics

Fall 2012

Topic for fall 2012: Introduction to mathematical finance.

Note: This course has been offered in alternate years. There is a similar course  at Umass (in the math department) which is offered every spring.

Instructor: Alan Durfee

• Office: Clapp 404B
• Telephone x2299 (with answering machine)
• email: adurfee
• Office hours: TBA

  Lectures: Monday, Wednesday, Friday 10:00-10:50 in Clapp 402.

• Course Description: An introduction to mathematical finance. Topics covered: interest rates, forwards and futures, options (in particular puts and calls), payoff diagrams, binomial trees, risk-neutral valuation,  geometric Brownian motion, Ito's lemma, the Black-Scholes PDE and formulas, implied volatility, volatility smiles, the Greeks, exotic options, and monte carlo methods. Concepts will be checked using data analysis on real life data.

• 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, 8th ed, Prentice-Hall (2012) . The 6th or 7th editions are OK too; the material we will do is covered in the same way in these editions.

  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. Your new score will replace the old one.

  Graders:

  • Mindan Chen (chen26m)
    
  • Hanh Hoang (hoang22h)
    

  Tests: There will be two in-class hour tests, one on (date to be decided), the other on (ditto). There will also be a self-scheduled final exam. If you are unable to take a test for any reason, you should let me beforehand (Email me, or call my office phone/answering machine anytime day or night.) Exams can always be taken early.

  Grading: Each test is 15%, the final is 25%, and homework is 45%.

  Books on reserve:

  • John Hull, Options, Futures and Other Derivatives, 8th edition (also 6th ed.)
    
  • Paul Wilmott, Paul Wilmott on Quantitative Finance
  • The Wall Street Journal Guide to Understanding Money and Investing. (A copy is also available at the Career Development Center)