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.
Background in Probability and Stochastic Calculus:
LINKS TO RELATED WEB SITES (under construction):
Please direct any questions to Professor Ruth J. Williams, email: email@example.com