Computer implementation is an essential component of
this subject, and you will be required to do some of your coursework
with computer programs. Either Matlab or Excel will be acceptable, but
we strongly encourage you to start with some basic
Matlab programming
if you have no prior experience with any computer programming.
This is the first part of a two-semester sequence course on mathematical finance.
In the Fall semester, we will examine the
fundamental principles of financial derivatives from
both financial and mathematical perspectives, and demonstrate how the
mathematical tools
from stochastic calculus, differential equations and numerical methods join forces
to form an essential
part in modern finance.
The emphasis of the course is a mathematical understanding
of the intrinsic relationships among
various financial instruments,
which serves as a basis for
investment decisions and trading strategies.
The central theme of
the Fall semester is the classic
Black-Scholes-Merton model, and
we plan to give a thorough treatment of the original model,
with
extensive discussions on the practical extensions in response to
various disadvantages of the original model.
One of
the most intuitive and transparent approaches to illustrate
that is also extensively used in
practice is the binomial tree model.
It contains most of
the essential idea of the Black-Scholes-Merton methodology, and
it can be naturally extended to build
more general continuous-time
models. Time permitting, we will include as much real life examples as
possible to make this
a rewarding experience for those who plan to
pursue a career in this direction, as well as those who are just
intrigued by the
subject and its impact on our society.
For Students Registered for Math 6890:
If you are a PhD student in a non-mathematics program, you may
register at the
6000 level. However, you will be required to do
extra work for the course which may include: more theoretical
exercises
in homework assignments and exams, and research
oriented projects. Grading curve for Math 6890 is separated from the
rest of the class.