MAT3104 Mathematical Modelling in Financial Economics
|Semester 2, 2013 On-campus Toowoomba|
|Faculty or Section :||Faculty of Sciences|
|School or Department :||Maths and Computing|
|Version produced :||8 December 2013|
Examiner: Ron Addie
Moderator: Dmitry Strunin
Pre-requisite: (MAT2100 and STA2300) or (MAT2500 and STA2300) or Students must be enrolled in the following Program: MSBN
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.
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. This course is offered only in odd numbered years.
On completion of this course students will be able to:
- understand how to analyse and make use of simple mathematical models of an economy;
- understand and apply stochastic processes of various types by means of simulation experiments;
- understand and apply binomial models of options and other financial instruments;
- solve and interpret classes of stochastic differential equations (SDEs);
- apply the equivalent martingale measure to a model of financial or economic activity in order to model risk;
- structure, prepare and deliver documents and presentations of technical material.
|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://bookshop.usq.edu.au/bookweb/subject.cgi?year=2013&sem=02&subject1=MAT3104)
Please contact us for alternative purchase options from USQ Bookshop. (https://bookshop.usq.edu.au/contact/)
Introductory Book 2013, Course MAT3104 Random Processes to Financial Mathematics, USQ Distance and e-Learning Centre, Toowoomba.
Study Book 2013, Course MAT3104 Random Processes to Financial Mathematics, USQ Distance and e-Learning Centre, Toowoomba.
Goodman, V & Stamfli, J 2001, The Brooks/Cole series in advanced mathematics, Brooks/Cole, Pacific Grove, CA.
Mishkin, F S 2002, The economics of money, banking, and financial markets, 6th ed edn, Addison-Wesley, Boston.
(Chapters 22 and 23.)
Oksendal, B K 1985, Stochastic differential equations, an introduction with applications, 5th ed 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.
Winston, W L 2004, Introduction to probability models: operations research volume II, Duxbury.
(Chapters 13-14 Operations Research Vol 2, 4th Edn.)
Student workload requirements
|Description||Marks out of||Wtg (%)||Due Date||Notes|
|ASSIGNMENT 1||10||10||09 Aug 2013|
|ASSIGNMENT 2||15||15||23 Aug 2013|
|ASSIGNMENT 3||15||15||13 Sep 2013|
|ASSIGNMENT 4||10||10||11 Oct 2013|
|2 HOUR OPEN EXAMINATION||50||50||End S2||(see note 1)|
- Examination dates will be available during the semester. Please refer to the examination timetable when published.
Important assessment information
It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) 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.
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.
Penalties for late submission of required work:
If students submit assignments after the due date without (prior) approval of the examiner then a penalty of 5% of the total marks gained by the student for the assignment may apply for each working day late up to ten working days at which time a mark of zero may be recorded. No assignments will be accepted after model answers have been posted.
Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.
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.
In an Open Examination, candidates may have access to any material during the examination except the following: electronic communication devices, bulky materials, devices requiring mains power and material likely to disturb other students.
Examination period when Deferred/Supplementary examinations will be held:
Any Deferred or Supplementary examinations for this course will be held during the next examination period.
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.
Students must retain a copy of each item submitted for assessment. If requested, students will be required to provide a copy of assignments submitted for assessment purposes. Such copies should be despatched to USQ within 24 hours of receipt of a request being made.
The due date for an assignment is the date by which a student must despatch the assignment to the USQ. The onus is on the student to provide proof of the despatch date, if requested by the Examiner. The examiner may grant an extension of the due date of an assignment in extenuating circumstances.
The Faculty will normally only accept assessments that have been written, typed or printed on paper-based media.
The Faculty will NOT accept submission of assignments by facsimile.
Students who do not have regular access to postal services or who are otherwise disadvantaged by these regulations may be given special consideration. They should contact the examiner of the course to negotiate such special arrangements.
In the event that a due date for an assignment falls on a local public holiday in their area, such as a Show holiday, the due date for the assignment will be the next day. Students are to note on the assignment cover the date of the public holiday for the Examiner's convenience.
Students who, for medical, family/personal, or employment-related reasons, are unable to complete an assignment or to sit for an examination at the scheduled time may apply to defer an assessment in a course. Such a request must be accompanied by appropriate supporting documentation. One of the following temporary grades may be awarded IDS (Incomplete - Deferred Examination; IDM (Incomplete Deferred Make-up); IDB (Incomplete - Both Deferred Examination and Deferred Make-up).