Derivative Securities
G63.2791, Fall 2004
Mondays 7:10–9:00pm
109 WWH
Instructor: Robert V. Kohn. Office: 612 Warren Weaver Hall. Phone: 998-3217. Email:
kohn@cims.nyu.edu. Office hours: Mondays 5-6pm, Wednesdays 5-6pm , after class or by
appointment. Web: www.math.nyu.edu/faculty/kohn.
Teaching Assistant: Paris Pender. Office: WWH 810. Phone: 998-3204. Email: pender@
cims.nyu.edu. Office hours: Thursdays 12:15-1:15 and Fridays 5-6.
Content: An introduction to arbitrage-based pricing of derivative securities. Topics include:
arbitrage; risk-neutral valuation; the log-normal hypothesis; binomial trees; the
Black-Scholes formula and applications; the Black-Scholes partial differential equation;
American options; one-factor interest rate models; swaps, caps, floors, swaptions, and other
interest-based derivatives; credit risk and credit derivatives.
Lecture notes: Lecture notes, homework assignments, etc. will be posted on my web page
in pdf format – normally within a day of when they are distributed. I’ll build a fresh set of
notes, homeworks, etc as we go along, but at the top of the course web page you’ll find a
link to the page built when I last taught the class, in Fall 2000. This fall’s version will be
similar, except that we’ll do one or two lectures on credit risk and credit derivatives near
the end of the semester.
Prerequisites: Calculus, linear algebra, and discrete probability. Concerning probability:
students should be familiar with concepts such as expected value, variance, independence,
conditional probability, the distribution of a random variable, the Gaussian distribution, the
law of large numbers, and the central limit theorem. These topics are addressed early in most
undergraduate texts on probability, for example K-L Chung and F. Aitsahlia, Elementary
probability theory : with stochastic processes and an introduction to mathematical finance
Springer 2003, on reserve in the CIMS library.
Course requirements: There will be approx 7 homework sets, one every couple of weeks.
Collaboration on homework is encouraged (homeworks are not exams) but registered students
must write up and turn in their solutions individually. There will be an in-class final
exam.The first class is Monday Sept 13; the last class is Monday Dec 13; the final exam is
Mon Dec 20.
Books: We will not follow any single book linearly. However to master the material of this
course you should expect to do plenty of reading. I recommend purchasing at least these
two books:
• J.C. Hull, Options, futures and other derivative securities, 5th edition.
• M. Baxter and A. Rennie, Financial calculus: an intoduction to derivative pricing,
Cambridge University Press, 1996.

The NYU bookstore has ordered about 30 copies of each; you may be able to save money by
buying them used. Earlier editions of Hull will be sufficient for this class, but the 5th edition
has some new sections on advanced or rapidly-developing topics like credit. These two books
go far beyond the scope of this course; roughly, they cover both Derivative Securities and
its spring sequel Continuous Time Finance.
Here are some additional books you may wish to buy or at least consult:
• R. Jarrow and S. Turnbull, Derivative securities, Southwestern, 2nd edition
• M. Avellaneda and P. Laurence, Quantitative Modeling of Derivative Securities, CRC
Press, 1999.
• P. Wilmott, S. Howison, and J. Dewynne, The mathematics of financial derivatives -
a student introduction, Cambridge University Press, 1995
• S. Neftci, An introduction to the mathematics of financial derivatives, Academic Press,
2nd edition.
• S. Shreve, Stochastic calculus for finance I: The binomial asset pricing model, Springer-
Verlag, 2004
All these books are on reserve in the CIMS library. Some brief comments: Jarrow-
Turnbull has roughly the same goals as Hull. I find it clearer on some topics, though
Hull is the industry standard. Wilmott-Howison-Dewynne is especially good for people
with background in PDE but unfortunately it de-emphasizes risk neutral valuation. Neftci
provides a good introduction to the most basic aspects of stochastic differential equations
and the Ito calculus (the first edition is sufficient for this purpose). Shreve’s book, hot off
the presses, is a lot like the first part of Baxter-Rennie, and a lot like the first half of this
course. (His Stochastic calculus for finance II: continuous-time models was just published;
it corresponds roughly to our classes Stochastic Calculus and Continuous Time Finance.)
An FAQ about probability: Math finance students often ask me for suggestions how to
enhance their knowledge of probability, for example in connection with the class Stochastic
Calculus. Professor Goodman is teaching Stochastic Calculus this fall, and he’ll undoubtedly
provide his own reading list. But here are some suggestions of my own:
(a) calculus-based probability. This material (at the level usually taught to upperlevel
math majors) is a prerequisite for Stochastic Calculus. There are many good
texts. The one by K-L Chung and F. Aitsahlia (Elementary probability theory with
stochastic processes and an introduction to mathematical finance, Springer-Verlag,
2003) has the advantage of including some material at the end that overlaps with
Derivative Securities. Earlier editions (by Chung alone) cover the probability without
the finance; they’re just as useful.
(b) more advanced probability books. Past students have found it useful to read
parts of the book by Z. Brzezniak and T. Zastawniak (Basic stochastic processes :
a course through exercises, Springer-Verlag, 1999) and/or the one by S. Resnick ((A
probability path, Springer-Verlag, 1999). The former includes a lot of material on

Markov chains; the latter includes an introduction to measure theory as it interfaces
with probability. Neither book covers stochastic calculus or its applications to finance.
(c) stochastic calculus. Students with relatively little background should certainly
look at S. Neftci’s book (An introduction to the mathematics of financial derivatives,
Academic Press), with the warning that it only scratches the surface. You might also
find T. Mikosch’s book ( Elementary stochastic calculus with finance in view) helpful,
but be warned that it’s more a list of facts than an explanation of them. Students with
sufficient background find J.M. Steele’s book a pleasure to read (Stochastic calculus
and financial applications, Springer-Verlag, 2001). The newest addition to the list
is Volume II of S. Shreve’s book (Stochastic calculus for finance II: continuous-time
models, Springer-Verlag, 2004). Its first half corresponds to our Stochastic Calculus
course; its second half is similar to our Continuous Time Finance course.
All the probability books suggested above are on reserve in the CIMS library (except
Mikosch, which is on order; it will go on reserve when it arrives).