The current and official versions of the course specifications are available on the web at https://www.usq.edu.au/course/specification/current.
Please consult the web for updates that may occur during the year.

# MAT3104 Mathematical Modelling in Financial Economics

 Semester 2, 2021 On-campus Toowoomba Short Description: Math Model Financial Economics Units : 1 Faculty or Section : Faculty of Health, Engineering and Sciences School or Department : School of Sciences Student contribution band : Band 1 ASCED code : 010101 - Mathematics Grading basis : Graded Version produced : 21 July 2021

## Staffing

Examiner: Trevor Langlands

## Requisites

Pre-requisite: (STA2300 or STA1003 or equivalent) and (MAT2100 or MAT2500 or ENM2600)

## Rationale

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 (SDEs) are of fundamental importance. SDEs also apply in many other areas in science and engineering and have many features that distinguish them from other mathematical models. Developing technical communication is also essential as preparation for the workplace which is addressed in this course.

## Synopsis

This course begins by investigating models of economic activity and the financial and economic strategies which are used to stimulate economic activity. After this 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 and scilab which are supplied on the course web page (students may choose whether to use R or scilab - it is not necessary to use both).
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 oncampus offering of this course is normally available only in odd numbered years. The external offering of this course is available yearly.

## Objectives

On completion of this course students 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

Description Weighting(%)
1. Macro-economic models 15.00
2. Simulation modelling of financial and stochastic processes 15.00
3. Binomial models of financial instruments (options and other contracts). 20.00
4. An introduction to Ito's stochastic calculus. The Black-Scholes model of European options and its solution. 20.00
5. Stochastic differential equations and their solution by means of Ito’s formula. 20.00
6. Martingale Models of Financial Markets and of Options 10.00

## Text and materials required to be purchased or accessed

ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (https://omnia.usq.edu.au/textbooks/?year=2021&sem=02&subject1=MAT3104)

Introductory Book (current year), Course MAT3104 Random Processes to Financial Mathematics, USQ Distance and e-Learning Centre, Toowoomba.
(Available on course StudyDesk.)
Study Book (current year), Course MAT3104 Random Processes to Financial Mathematics, USQ Distance and e-Learning Centre, Toowoomba.
(Available on course StudyDesk.)

## Reference materials

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.
Goodman, V & Stamfli, J 2001, 'The brooks/Cole series in advanced mathematics', The mathematics of finance:modelling and hedging, Brooks/Cole, Pacific Grove, CA.
(Chapters 1-3.)
Mishkin, F S 2018, The economics of money, banking, and financial markets, 12th edn, Addison-Wesley, Boston.
(Chapters 22 and 23.)
Oksendal, B K 2007, Stochastic differential equations, an introduction with applications, 6th edn, Springer, Berlin.
(Chapters 1-3 & 12.)
Wilmott, P, Howison, S & Dewiynne, J 1995, The mathematics of financial derivatives, a student introduction, Cambridge University Press. Oxford.
(Chapters 1-4.)
Winston, W L 2004, Introduction to probability models: operations research volume II, Duxbury.
(Chapters 13-14 Operations Research Vol 2, 4th Edn.)

Activity Hours
Assessments 42.00
Online Lectures 26.00
Private Study 78.00
Tutorials 26.00

## Assessment details

Description Marks out of Wtg (%) Due Date Notes
ASSIGNMENT 1 10 10 05 Aug 2021
ASSIGNMENT 2 15 15 19 Aug 2021
ASSIGNMENT 3 15 15 09 Sep 2021
ASSIGNMENT 4 10 10 07 Oct 2021
PROBLEM SET 50 50 18 Oct 2021 (see note 1)

Notes
1. This assessment will include a written submission and an online viva voce via zoom. Full details will be available on the course Study Desk.

## Important assessment information

1. Attendance requirements:
It is the students' responsibility to participate appropriately in all activities scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.

2. Requirements for students to complete each assessment item satisfactorily:
To complete each of the assessment items satisfactorily, students must obtain at least 50% of the total marks available for each assessment item.

3. Penalties for late submission of required work:
Students should refer to the Assessment Procedure http://policy.usq.edu.au/documents.php?id=14749PL (point 4.2.4).

4. Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must obtain at least 50% of the total weighted marks available for the course (i.e. the Primary Hurdle).

5. Method used to combine assessment results to attain final grade:
The final grades for students will be assigned on the basis of the weighted aggregate of the marks obtained for each of the summative assessment items in the course.

6. Examination information:
There is no examination for this course.

7. Examination period when Deferred/Supplementary examinations will be held:
Deferred and Supplementary examinations will be held in accordance with the Assessment Procedure https://policy.usq.edu.au/documents/14749PL.

8. University Student Policies:
Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene University policies and practices. These policies can be found at http://policy.usq.edu.au.

## Other requirements

1. Computer, e-mail and Internet access:
Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at http://www.usq.edu.au/current-students/support/computing/hardware .

2. Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.

Date printed 21 July 2021