Offering Information
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Course Team
Trevor Langlands
Harry Butler
Summary
Of fundamental importance to science, finance and engineering, are processes with random fluctuations. The series of prices of a financial instrument such as an equity, bond, or contract is an ideal and extremely important example. Some graduates will work in financial and commercial applications of mathematics where stochastic differential equations … For more content click the Read More button below.
SynopsisThis course begins by investigating models of economic activity and the financial and economic strategies which are used to stimulate economic activity. After these models of financial processes, such as equity prices, interest rates, bond yields, and so on are considered. Simulation models of such processes are developed and used in experiments using scripts written in R which are supplied on the course web page.
The theory of Stochastic differential equations is introduced and studied by simulation and in theory. Techniques for solving such equations by means of Ito's formula are explained and applied. This is applied to financial process problems and the Black-Scholes differential equation is formulated and solved. Binomial tree models are introduced and used to solve a variety of option pricing models. In the last part of the course the method for solving option pricing problems based on the equivalent martingale measure.
The theory of Stochastic differential equations is introduced and studied by simulation and in theory. Techniques for solving such equations by means of Ito's formula are explained and applied. This is applied to financial process problems and the Black-Scholes differential equation is formulated and solved. Binomial tree models are introduced and used to solve a variety of option pricing models. In the last part of the course the method for solving option pricing problems based on the equivalent martingale measure.
Requisites
Course Pre-requisites
Course Pre-requisites
Other Requisites or Enrolment Rules
Other
Offerings
Trimester 2
OL-TWMBA-TR2
ON-TWMBA-TR2
Learning Outcomes
Upon completion of this course, graduates will be able to:
1.
examine how to make use of simple mathematical models of an economy
2.
simulate stochastic processes of various types, using provided software, and interpret the results;
3.
apply mathematical models of financial or economic activity to model risk;
4.
solve and interpret stochastic differential equations (SDEs);
5.
prepare, for a general audience (not just mathematicians), documents and presentations of technical material both individually and in collaboration with other students.
Topics
Macro-economic models (15%)
Simulation modelling of financial and stochastic processes (15%)
Binomial models of financial instruments (options and other contracts) (20%)
An introduction to Ito's stochastic calculus. The Black-Scholes model of European options and its solution (20%)
Stochastic differential equations and their solution by means of it's formula (20%)
Martingale … For more content click the Read More button below.
Assessments
Assessment due dates (as listed in Week Due) are indicative until finalised by the end of Week 1 for each Study Period (Offering). After Week 1, Assessment due dates may change with the approval of the Dean (Academic) or Delegate in limited circumstances. All Assessment due date changes approved after Week 1 will be communicated to students accordingly via Handbook and StudyDesk.