Math 458/558 Mathematical Finance - Fall 2009 revised Aug 31

Office hours: 11:00-12:00, and by appointment.

Course Description: Mathematical models and solution methods for a number of important concepts in mathematical finance: mean-variance portfolio theory, the capital asset pricing model, derivative securities, asset dynamics, and the Black-Scholes equation for options pricing. The course does not assume extensive mathematical background as the necessary mathematical theory is introduced in the context of the financial models. The mathematical aspects of the course include probability and statistics, optimization, models for asset dynamics (discrete and continuous), random variables, stochastic differential equations, and solution methods for the Black-Scholes partial differential equation for option pricing.

Course website: www.math.buffalo.edu/~hassard/458-558/

Text: Investment Science by D. G. Luenberger, (Oxford Press, 1998) Chapters 1, 6-8, 11-13.

Prerequisites: Calculus, elementary differential equations. Familiarity with (or willingless to learn to use) a spreadsheet program on a computer.

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 and late homework will not be accepted.

Exams: There will be two exams. 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. There will NOT be a Final Examination during the Examination Period.

Grading: There are 400 points available: 100 points for exam 1, 100 points for exam 2 and 200 points for the homework. 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 extreme situations (ex/ non-elective surgery) and you must be passing the course to receive an incomplete.

Assignments to date http://www.math.buffalo.edu/~hassard/458-558/458-558fa09hw.php

Topics (tentative):

• Introduction: cash flows, investments and markets, comparison, arbitrage, dynamics, risk, pricing, hedging, random cash flow streams, derivative securities.
• Mean-variance Portfolio Theory: asset return, random variables, random returns, portfolio mean and variance, Markowitz minimum variance portfolio, two-fund theorem, inclusion of a risk-free asset, one fund theorem.
• Capital Asset Pricing Model (CAPM): market equilibrium, market lines, performance evaluation, CAPM as a pricing formula.
• Models and Data: data and parameter estimation.
• Models of Asset Dynamics: binomial lattice model, introduction to stochastic differential equations (random walks, Ito's lemma, connection to lattice models).
• Basic Options Theory: basic options, put-call parity.
• Black-Sholes Equation for Option Pricing: derivation of the Black-Scholes equation, analytical solutions for special cases, numerical solutions (Monte Carlo, lattice and finite difference solutions).

MTH 558: 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.

Important Dates:
Fri Sep 4	Last day to drop the course - no record appears on transcript. Last day to file 'Petition to make up an incomplete' with the Department.
Mon Sep 7	class cancelled (Labor Day)
Fri Sep 18	HW1 due
Mon Sep 28	class cancelled (Yom Kippur)
Fri Oct 2	HW2 due
Wed Oct 14	Exam 1
Wed Oct 21	HW3 due
Fri Nov 13	HW4 due
Fri Nov 13	Last day to resign from the course - an 'R' appears on transcript.
Wed Nov 25- Fri Nov 27	class cancelled (Fall recess)
Mon Nov 30	HW5 due
Wed Dec 9	Exam 2
Fri Dec 11	Last day of the class

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.