INSTRUCTOR. Prof. Irene Hueter, Rm 4-255 Vertical Campus, Phone (646) 312-4169, Fax (646) 312-4111,
irene_hueter@baruch.cuny.edu , http://www.math.baruch.cuny.edu/~ihueter/ .OFFICE HOURS. Mondays 12:30-1:30PM, Wednesdays 8:00-9:00AM, and by appointment.
AIMS OF THIS COURSE. The course is aimed at getting the students acquainted with some of the basic ideas in options pricing, the Black-Scholes theory, present value analysis, maximizing expected utility, and exotic options. In the group projects especially, the students are invited to reflect about the suitability of the underlying model and try more elaborate models in conjunction with live market data and historical data available at Baruch's Subotnick Financial Services Center (SFSC) and the real-time financial Trading Floor (see http://aux.zicklin.baruch.cuny.edu/sfsc/).
INSTRUCTIONAL FORMAT. Mostly lectures by the instructor. Everyone is strongly encouraged to participate in the class activities and ask questions. Towards the end of the semester, the students will be asked to present their projects.
TEXT.
An Elementary Introduction to Mathematical Finance.
Options and Other Topics. (Second Edition),
by Sheldon M. Ross, Cambridge University Press, 2003,
ISBN: 0-521-81429-4. FURTHER READING.
The Mathematics of Financial Derivatives. A Student Introduction.
Paul Wilmott, Sam Howison, Jeff Dewynne, Cambridge University Press,1995.
ISBN: 0-521-49789-2. PREREQUISITES.
Working knowledge of Calculus II or permission of instructor.
Some familiarity with probability and statistics is helpful,
but not necessary, as well as some familiarity with programming.
MATERIAL TO BE COVERED.
See below. HOMEWORK.
Homework will be assigned
(click here)
in nearly every class.
A selection of these will be discussed in a subsequent
class. The students will have the opportunity to present
solutions to the problems in class.
Homework problems are not collected and do
not count towards your final grade.
Yet working the homework problems, without which you
will not learn the material, is essential to your
success in this course and is one of the best ways to
prepare for the exams. Solve as many homework problems
as possible. PROJECTS.
In groups of 3 to 4, students will design and carry out a project,
related to the course, and turn in a written paper, describing the
project activities, by
May 10 .
A project proposal is due by
March 24 .
The projects will be graded on the merits of creativity, interest,
suitability of model and analysis, clarity and writing style.
The project together with the in-class presentation will be worth
one third of the final grade, thus, worth 100 points. TESTS.
There will be one midterm and one comprehensive final
exam, each worth 100 points. EXAM SCHEDULE.
The SFSC regularly offers the Reuters I
and Reuters II workshops
that include "hands-on interaction with real-time and
historical market data through Reuters 3000 Xtra." The
workshops are open enrollment for all current Baruch students,
undergraduate and graduate.
For the schedule, visit the "Calendar" at
http://aux.zicklin.baruch.cuny.edu/sfsc/.
Important:
(1)
For makeups, you must have proper
written documentation, provided close in time to the exam to
be missed.
(2)
According to department policy, any student who scores less than
50 % on the final exam may not receive a passing grade.
Any student who is absent from the final exam and whose term
average is at least 55 % is given a final grade of ABS.
The student must present a valid excuse to the Office of Curricular
Guidance and apply for a make-up final exam. If the term average
is less than 55 %, the student is given an F grade.
The exam dates may change as the semester progresses.
For the answers to the Take-Home Final (Pdf)
(click here).
SPRING RECESS. April 2 - 13, 2004.
OTHER IMPORTANT DAYS.
February 16: Presidents' day. College closed.
February 20: Last day to drop without 'W' grade.
April 15: Last day to withdraw with 'W' grade.
May 19: Last day of classes.
May 20-27: Final Examinations' week.
ATTENDANCE. The instructor will take attendance. Excessive unexcused absences may lead to a failing grade.
CELL PHONES. All cell phones should be turned OFF. Be aware that your cell phone at work is very disruptive to the class, your fellow students, and the instructor. If you expect an emergency call, please clear it with me before class. If a cell phone rings during class or an exam, the student will be asked to leave for the remainder of the class or exam (and to turn in the exam).
ACADEMIC HONESTY. This class falls under Baruch College's Academic Honesty policy. Academic dishonesty is unacceptable, will not be tolerated, and entails sanctions since it undermines the college's educational mission and the students' personal and intellectual growth. Please inform yourself of the principles and rules at http://www.baruch.cuny.edu/academic/academic_honesty.html. Be aware that ignorance of the guidelines are not an excuse and that academic dishonesty may have severe consequences in your student career.
GRADING.
The grade will be based on your performance in your 2 exams (200 points) and
your project and presentation (100 points).
Maximal score = 300 points = 100 %. GETTING HELP.
The following are crucial factors to your success in this class:
attend class regularly, read upcoming sections ahead of time so
that you are prepared to ask questions in class, start homework
early (the day before an exam is too late), and get help when there are
signs of difficulties (during the class, even after, and while solving homework
questions). Please make regular use of office hours.
A (93.0 - 100 %), A- (90.0 - 92.9 %), B+ (87.1 - 89.9 %),
B (83.0 - 87.0 %), B- (80.0 - 82.9 %), C+
(77.1 - 79.9 %), C (73.0 - 77.0 %), C- (70.0 - 72.9 %),
D+ (67.1 - 69.9 %), D (60.0 - 67.0 %), F (< 60.0 %).
Week(s) Topics
1 An Introduction to Options and Markets:
What is an option ? What is an option for ? Various types of options.
Forward and futures contracts. Simple examples in options pricing.
Concept of arbitrage. No free lunch.
2 Interest Rates and Present Value Analysis:
Interest rates, present value analysis, rate of return, continuously
varying interest rates.
3, 4 Introduction to Probability:
Probability and events, conditional probabilities.
Discrete and continuous random variables.
Expectation, variance, covariance, correlation.
Normal random variables and their properties, Central Limit theorem.
Lognormal random variables.
5 Geometric Brownian Motion:
Brownian motion, geometric Brownian motion.
Testing the model assumption for data. Goodness of fit.
6 Pricing Contracts via Arbitrage:
An example in options pricing, put-call option parity,
American call option never optimal to exercise.
Forwards contracts, generalized law of one price.
7 Arbitrage Theorem:
Arbitrage theorem, multiperiod binomial model.
8, 9 Black-Scholes Option Pricing Formula:
Black-Scholes option pricing formula, for put and call options,
dependence on underlying parameters: stock price, expiration time,
strike price, volatility, and interest rate.
Delta hedging. Estimating the volatility from data.
Implied volatility, volatility smile. Goodness of fit, free lunch (?).
SPRING BREAK
10 Review and Midterm Exam.
11 More Results on Options:
Call options on dividend-paying securities.
Adding jumps to the geometric Brownian motion.
When the option cost differs from the Black-Scholes formula.
12 Valuing by Expected Utility:
Valuing investments by expected utility, portfolio selection problem.
13 Exotic Options:
Barrier options, Asian and lookback options, pricing options
by simulation.
14, 15 Student Presentations, Review, and 'What else could have been covered.'