Math 459/559 Mathematical Finance 2 - "Spring" 2013

Instructor: Jim Reineck, 208 Mathematics Building, 645-8774, reineck@buffalo.edu. My office hours are TuTh 11:00-12:20, and by appointment. Please do not hesitate to make an appointment if you have questions. Just ask me after class and we can set up a time.

Location: The lectures are TuTh, 9:30-10:50, in 250 Mathematics

Course website: http://www.math.buffalo.edu/~reineck/m559.html.
Assignments

nonlinear risk spreadsheet
Here are price simulations: daily   weekly   monthly .
Lattice Options Pricing Spreadsheet is here .
Maple worksheet for Monte Carlo call is here .
Monte Carlo spreadsheet for varying mu is here .
Newton's method spreadsheet is here .
Lattice Options Pricing Spreadsheet is here .
Implied Volatility Worksheets: Cisco   Google .
Confidence interval worksheets: constant N   increasing N.

Course Description: The course will cover utility functions, forwards, futures, swaps and various aspects of options pricing. Some discussion of numerical methods will be included.

Prerequisites: Math 458 or 558.

Texts:

• Investment Science, by D. G. Luenberger, (Oxford Press, 1998), Chapters 9-10.
  
• An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, by Desmond J. Higham, (Cambridge Univ. Press, 2004), Chapters 4, 12-15, 17-24.

Topics (tentative):

• Utility functions.
• Forwards, futures, and swaps.
• Computer Simulation: pseudo random numbers, numerical solution of equations, Monte Carlo methods.
• Risk Neutral Pricing and Implied Volitility.
• American Options: Black-Scholes, the optimal exercise boundary, and Monte Carlo methods.
• Dividends: The effect of continuous and discrete dividend payments on option prices.
• Exotic Options: digital options, lookback options, barrier options, Asian options, maybe more.
• Historical Volitility and Monte Carlo methods: estimation of parameters and variance reduction.
• Finite Difference methods: forward and backward Euler method, Crank-Nicholson, application to Black-Scholes.

Homework: With each lecture there will be assigned homework. Some of the questions will be identified as an assignment to be turned in with a specified due date and then graded. Each problem to be graded will have a point value (5, 10, 15, ...) based on difficulty. For each homework question, write a clear exposition of your solution (including sentences to explain your work where appropriate). To make it easier for record keeping, include the following information: name, MTH 458 or MTH 558, assignment due date. Homework is due at the beginning of class on the day stated (late homework will not be accepted). The cumulative homework score will be graded on a curve to determine the homework grade for the course.

Exams: There will be two exams. There will be no final exam during the exam period.

• The First Exam will be in March, most likely the week before Spring Break. The precise date will be announced well in advance of the exam.
• The Second Exam will be on the last day of class, Thursday, April 25th.

You are permitted one 3"x5" notecard with notes/formulas for each exam. Material covered in the exam is anything in the book or presented in lecture. The exam will consist of a mix of questions: some easy, some hard, and may also contain essay-answer questions. Each exam will be graded on a curve.

MTH 559: In accordance with Graduate School policy regarding dual-listed 400/500 level courses, students taking the course for graduate credit will be assigned additional or more difficult homework questions and will have additional or more difficult questions on exams. Grades for graduate students will be assigned based on graduate school standards.

Academic Honesty: You are expected to adhere to the letter and spirit of academic honesty. For homework assignments, you can discuss assignments with other students, but the details of the written solution as turned in are originally yours. Cheating or misrepresentation of your own work will result in formal charges being initiated and pursued to the fullest extent possible. You must have your student ID for all exams.

Grades: There are 400 points available:
Exams: 100 points each
Homework: 200 points.
There will be a curve for each exam and for the homework. Basically, if your sum is greater than or equal to the sum of the A cutoffs, you will receive an A. If your sum is between the sum of the B cutoffs and the sum of the A cutoffs, you will receive a B, etc. However, I will use +/- in the final grades. If your sum is just below (e.g. within 5 points) of the A cutoff, you will get an A-. If you are just below this, you will get a B+, etc. Incompletes will be given only in the most extreme emergencies, e.g. surgery the last week of the course. Please note that you must be passing the course to receive an incomplete.

Important Dates:
Sat Jan 19th - Last day to drop the course without financial or academic penalty.
Tue Jan 22nd - Last day to add the course.
Tue Mar 12th, Th Mar 14th - Spring Break, no class.
Fri Mar 29th - Last day to resign from the course - an 'R' appears on transcript.
Thu Apr 25th - Last day of the course and Second Exam.

Students with disabilities: If you have a diagnosed disability (physical, learning or psychological) which will make it difficult for you to carry out the course work as outlined, or requires accommodations such as recruiting note takers, readers or extended time on exams and/or assignments, please advise me during the first two weeks of the course so that we may review possible arrangements for reasonable accommodations.

Watch this space for important announcements.