MATH5975 is a Mathematics Level V course. See the course overview below.

Units of credit: 6

Prerequisites:

Cycle of offering: yearly in Semester 1.

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: this recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH5975, you can log into the My eLearning Vista instance of this course.

Modern theory of financial markets relies on advanced mathematical and statistical methods that are used to model, forecast and manage risk in complex financial transactions. After the publication in 1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing of European call options, it became clear that Stochastic Analysis is an indispensable tool for the theory of financial markets, derivation of prices of standard and exotic options and other derivative securities, hedging related financial risk, as well as managing the interest rate risk.

In this course, you will learn the basic concepts and techniques of Stochastic Analysis, such as: Brownian motion, martingales, Ito stochastic integral, Ito's formula, stochastic differential equations, equivalent change of a probability measure, integral representation of martingales with respect to a Brownian filtration, relations to second order partial differential equations, and the Feynman-Kac formula.

Some concepts will be illustrated by examples relevant for financial applications. However, the main goal of the course is to provide a necessary mathematical background for MATH5816 Continuous Time Financial Modelling and MATH5985 Term Structure Modelling, rather then to focus directly on financial concepts.