Revised January 27, 2003
22:390:652
Spring 2003
Advanced Derivatives
Rutgers Business School – Newark and New Brunswick
COURSE DESCRIPTION
This course will cover (1) exotic options, (2) interest rate derivatives, (3) real options and (4) insurance,
weather and energy derivatives. We will spend the most time on interest rate derivatives.
TIME
Monday evenings, from 6:00 to 9:00 pm., with a break from 7:30 to 7:45.
PLACE
Global Financial Market Center,1st Floor, Ackerson Hall, 180 University Avenue, Newark Campus.
INSTRUCTOR
Glenn Shafer, 302C Ackerson Hall, Newark.
Phone 973-353-1604, fax 1283, secretary (Jackie Adams) 1644, home 973-483-1692, fax 1693
www.glennshaer.com
gshafer@andromeda.rutgers.edu
OFFICE HOURS
Mondays 4:30 to 5:30 and by appointment.
REQUIRED BOOKS
• Options, Futures, and Other Derivatives, by John C. Hull, 5th edition, 2002. YES, YOU NEED
THE 5TH EDITION, because we will cover chapters not in the 4th edition.
• Solutions Manual. This manual provides answers to most of the problems that Hull gives at the
ends of his chapters, but not the ones I assign for homework. My experience has been that
students find it invaluable for preparing for examinations.
PREREQUISITES AND PHILOSOPHY
This is the first time this course has been offered at Rutgers. Enrollment comes from two different groups:
1. MBA students who have already completed a first course in options and derivatives, covering the
earlier chapters in Hull’s book.
2. MQF (masters of quantitative finance) students who may have a stronger background in
theoretical finance but may not have had the first course in options and derivatives.
I will teach the course this semester in a way that accommodates both groups of students. In other words,
you need either (1) a first course in options and derivatives or (2) the mathematical sophistication of an
MQF student, but not both.
Students who took 22:390:609 using Hull’s book may regard this course as a continuation on into later
chapters of the book. There is a change of tone, however, because these later chapters require a more
thorough understanding of the material in Hull’s Chapters 11 and 12: the Wiener process, Itô’s lemma, the
Black-Scholes equation, and risk-neutral valuation. These topics are usually covered only lightly in the
first course.
In order to get everyone onto the same page, my lectures during the first few weeks will review and go
deeper into topics already familiar to some students:
• Primarily for the benefit of the MQF students, I will some lecture time during the first four weeks
reviewing topics from 22:390:609. These topics will include pricing forwards, forward rates,
pricing swaps, put-call parity, and the so-called Greek letters in option pricing.
• Primarily for the benefit of the MBA students, I will go more deeply into Hull’s Chapters 11 and
12 (geometric Brownian motion, Ito’s formula, and risk-neutral pricing) than is done in the first
course.
Revised January 27, 2003
LECTURES
Hull provides excellent lecture slides on his web site, http://www.mgmt.utoronto.ca/~hull/. I recommend
that students print out these slides for the chapters being covered in class and bring them to class each
week, because I will often use them in my lecture. I will often provide additional slides as well.
HOMEWORK AND EXAMINATIONS
I will collect your homework the week after it is assigned and return it the following week. I will
sometimes discuss the homework problems in class before collecting them, but I cannot distribute
solutions, because other classes will be using the same problems in future semesters. Because I do not have
a lot of time to study your solutions, clarity of presentation will be an important component of your grade.
The examinations will cover all the material in the assigned chapters, not merely topics that are reinforced
by the homework. The examinations will be closed-book, but you should bring a calculator. You may
bring two 8 ½ x 11 sheets of paper with notes on both sides.
SUPPLEMENTARY BOOKS?
Hull’s book is truly extraordinary. It explains mathematically complicated concepts in an accurate but
understandable way, adds a great deal of necessary institutional information, and tops it off with very
useful exercises. Moreover, each successive edition has cast a wider net. It is no wonder that the book is
so widely used by professionals as well as in university classrooms. I cannot recommend with the same
enthusiasm any other book at the same level. However, there are three books that I can recommend to
students who want to look at other perspectives:
• For more on interest-rate products, see Understanding and Managing Interest Rate Risks, by RenRaw Chen (a professor in our school), World Scientific, 1996.
• For a more mathematical exposition of the stochastic calculus and its application to interest-rate
products, see Financial Calculus, by Martin Baxter and Andrew Rennie, Cambridge, 1996.
• For a different perspective on the stochastic calculus, see Probability and Finance: It’s Only a
Game!, by Glenn Shafer and Vladimir Vovk, Wiley, 1996.
GRADING
Homework
Midterm
Comprehensive Final
40%
20%
40%
TENTATIVE SCHEDULE AND HOMEWORK ASSIGNMENTS
(Except for the inclusion of review topics, this schedule is very close to the one Hull uses for his course in
advanced derivatives; see his outline at http://www.rotman.utoronto.ca/~hull/2307out/.)
Week 1. January 27
• Chapter 11 (including Appendix 11A) The Stochastic Calculus
• Review: pricing forwards (Chapter 3), put-call parity (8.4)
• Homework due next week: Chapter 11 problems 13, 14, 15, 16, plus handout
Week 2. February 3
• Chapter 12 (including Appendix 12A) The Black-Scholes Equation
• Review: Greek letters (Chapter 14)
• Homework due next week: 12.26, 12.29, 14.18, 14.30
Week 3. February 10
• Chapter 10 and sections 18.1-18.5 of Chapter 18 Binomial Trees
• Review: forward rates (Chapter 5)
Revised January 27, 2003
•
Homework due next week: Chapter 18 problems 25, 27, 29, 30
Week 4. February 17
• Chapter 17 Estimating Volatilities and Correlations
• Chapter 18 (18.6-18.8 only) Numerical Procedures
• Review: pricing swaps (Chapter 6)
• Homework due next week: 17.15, 17.17, 18.28
Week 5. February 24
• Chapter 19 Exotic Options
• Homework due next week: Chapter 19 problems 23, 25, 27, 28
Week 6. March 3
• Chapter 20 More on Models and Numerical Procedures
• No homework will be collected next week, but Chapter 20 will be included on the midterm.
Week 7. March 10
• 6:00—7:30 Introduction to Chapter 21 Martingales and Measures
• 7:45—9:00 Midterm Examination
March 17. Rutgers Spring Break
Week 8. March 24
• Chapter 21 Martingales and Measures (continued)
• Homework due next week: Chapter 21 problems 16, 17, 18
Week 9. March 31
• Chapter 22 Interest Rate Derivatives: The Standard Market Models
• Homework due next week: Chapter 22 problems 27, 29, 31, 32
Week 10. April 7
• Chapter 23 Interest Rate Derivatives: Models of the Short Rate
• Homework due next week: Chapter 23 problems 24, 25, 26, 27
Week 11. April 14
• Chapter 24 Interest Rate Derivatives: More Advanced Models
• Homework due next week: Chapter 24 problems 16, 17
Week 12. April 21
• Chapter 28 Real Options
• Homework due next week: Chapter 28 problems 9, 10
Week 13. April 28
• Chapter 29 Insurance, Weather, and Energy Derivatives
• No homework will be collected next week, but Chapter 29 will be included on the final.
May 5. Final Examination
• This examination will cover all the material in the course, including the material already covered
in the midterm.