MATH 294            THE MATHEMATICS OF FINANCE       WINTER 1999 

DESCRIPTION:
This course is an introduction to the mathematics of financial models. 
The aim is to provide students with an introduction to some basic 
models of finance and the associated mathematical machinery.


OUTLINE: 
The course will roughly follow the topics covered in the text 
"Financial Calculus" by Baxter and Rennie.
The treatment of that book will be supplemented with mathematical background 
and details
as needed. The supplementation will draw on a variety of sources including other
texts and journal articles. In addition, structured computer modules
to illustrate the theoretical material will accompany the course.

The course will begin with the development of the basic ideas of hedging and 
pricing by arbitrage
in the discrete time setting of binomial tree models. 
Key probabilistic concepts of conditional
expectation, martingale, change of measure, and representation, 
will all be introduced first in this
simple framework as a bridge to the continuous model setting.
Mathematical fundamentals for the development and analysis of continous time
models will be covered, including Brownian motion, stochastic calculus, change
of measure, martingale representation theorem. These will then be combined
to develop the Black-Scholes option pricing formula. 
This model with then be adapted and applied to price various market securities
including dividend paying equities, currencies and coupon paying bonds.
Attention will then turn to models of the interest rate market.
Various models will be discussed, including the several Heath-Jarrow-Morton type
models and the Cox-Ingersoll-Ross model. As time permits, more general
models and extensions will be described.  


COMPUTER MODULES:
These will complement the theoretical material presented in the course.
Students may wish to enrol in 
Math 161 in the Fall of 1998, which will include an Introduction to Mathematica.
(This  course for two-four units meets 3 hours per week -- the schedule
indicates that an EXTRA 3 lab hours/week will be required -- this is
INCORRECT.)


REFERENCES:

Financial calculus, Martin Baxter and Andrew Rennie, Cambridge University Press,
1996. 

J. Hull, Options, Futures and other Derivative Securities (Prentice Hall, 93)

An Introduction to the Mathematics of Financial Derivatives,
Salih N. Neftci, Academic Press, 1996.

The Mathematics of Financial Derivatives: A student introduction, Paul Wilmott, et al., Cambridge
University Press, 1995.