**
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 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.
Pricing and hedging for European and American call
options will be discussed.
If time allows, attention will then turn to models of the interest rate market.
Various models may be discussed, including the
Heath-Jarrow-Morton
and Cox-Ingersoll-Ross models.

** PREREQUISITES: ** A course in probability or consent of instructor.
A possible probability course is Math 280AB (Graduate Probability).
However, other probability courses may be used in place of this with the
consent of the instructor.
The course
Math 286 (Stochastic Differential Equations) is a very useful
complement to Math 294 and students may find it helpful to take Math 286
before or after Math 294.

** COMPUTER MODULES: **
These will complement the theoretical material presented in the course.

** TEXT: **
Martingale methods in financial modelling,
M. Musiela and M. Rutkowski, Springer, 1998.

** REFERENCES: **

* Background in Probability and Stochastic Calculus: *

** LINKS TO RELATED WEB SITES (under construction):**

Please direct any questions to Professor Ruth J. Williams, email: williams@math.ucsd.edu