Course coordinator
Dr Kazutoshi Yamazaki
Course overview
- Study period
- Semester 1, 2025 (24/02/2025 - 21/06/2025)
- Study level
- Postgraduate Coursework
- Location
- St Lucia
- Attendance mode
- In Person
- Units
- 2
- Administrative campus
- St Lucia
- Coordinating unit
- Mathematics & Physics School
Introduction to financial mathematics and its applications. Mathematical models of annuities, equity and fixed-income products, futures and forward contracts, the term structure of interest rates and investment returns.
This course is an introduction to financial and actuarialﾠmathematics. It introduces basic concepts and principles in finance and basic mathematical and statistical tools used by financial mathematicians and actuaries. Topics covered will include a selection from the following: compound interest and annuities, discounted cashflow valuation, risk and return, fixed interest securities, valuation by arbitrage and replication, derivative securities including futures, swaps and options, the term structure of interest rates, stochastic models for investment returns, modern portfolio andﾠfinancial theory, risk management.
In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is crucial for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.
Bullying, harassment, and discrimination in any form are strictly against our principles and against UQ Policy, and will not be tolerated. We have developed a suite of resources to assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us.
Course requirements
Assumed background
The course assumes some knowledge of calculus, linear algebra, probability,ﾠandﾠstatistics at a level typically provided in MATH1051, MATH1052, andﾠSTAT2003 and/or STAT2004.ﾠﾠStudents with alternative backgrounds should discuss this with the coordinator.ﾠ Students should also be relatively familiar with MATLAB programming.
Incompatible
You can't enrol in this course if you've already completed the following:
MATH3090 or MN391
Jointly taught details
This course is jointly-taught with:
MATH3090 and MATH7039 are co-badged courses and will share learning activities. MATH7039 will have some differences in assessment to evaluate students at Level 9 (Masters) of the Australian Qualifications Framework.
Course contact
Course staff
Lecturer
Dr Kazutoshi Yamazaki
Tutor
Mr Chang Chen
Mr Jay Parfitt
Mr Jacob Westerhout
Timetable
The timetable for this course is available on the UQ Public Timetable.
Additional timetable information
All classes will be conducted on campus at the times and location advertised in your personal timetable.
Important: If you are ill, then do not attend any classes in person. Alternative arrangements can be organised – consult Blackboard for details.
Aims and outcomes
MATH7039 will give
- An introduction to basic concepts, principles and language used in financial markets and financial theory.
- An introduction to the mathematical and statistical tools and techniques used by finanical mathematicians and actuaries to price financial products and model financial risk.
Learning outcomes
After successfully completing this course you should be able to:
LO1.
Interest Rates and Annuities - Understand the fundamental nature of financial markets and the role played by financial mathematicians
LO2.
Interest Rates and Annuities - Model the cash flows of a range of financial contracts in discrete and continuous time
LO3.
Interest Rates and Annuities - Understand and derive the relationships between interest rates across different time periods
LO4.
Interest Rates and Annuities - Define, derive and use the compound interest functions of relevance to financial mathematicians
LO5.
Stochastic and Financial Modeling - Define and use an equation of value when cash flows are uncertain
LO6.
Stochastic and Financial Modeling - Show how both discrete- and continuous-time discounted cash flow techniques can be used to appraise investments
LO7.
Stochastic and Financial Modeling - Mathematically describe the investment characteristics of fixed income assets (debt), equity (shares) and financial derivatives
LO8.
Stochastic and Financial Modeling - Understand arbitrage pricing and use arbitrage pricing for futures/forwards and swap contracts
LO9.
Stochastic and Financial Modeling - Understand the term structure of interest rates
LO10.
Stochastic and Financial Modeling - Understand and derive simple stochastic interest rate models
LO11.
Options and the Black-Scholes Model - Understand the defining characteristics of options and options markets
LO12.
Options and the Black-Scholes Model - Understand the notion of risk-neutral pricing and the fundamental theorems of asset pricing in a simple one-period setting
LO13.
Options and the Black-Scholes Model - Have a basic appreciation and understanding of the derivation of the Black-Scholes model by the heat equation
LO14.
Options and the Black-Scholes Model - Understand how the notions of arbitrage and replication are used in the derivation of the Black-Scholes model
LO15.
Portfolio Construction and Analysis - Derive and understand simple stochastic models for equity (shares)
LO16.
Portfolio Construction and Analysis - Derive and understand the main results of modern portfolio theory
LO17.
Portfolio Construction and Analysis - Define and identify a coherent risk measure
LO18.
Portfolio Construction and Analysis - Define and understand the role of risk measures in the management of risky assets
Assessment
Assessment summary
| Category | Assessment task | Weight | Due date |
|---|---|---|---|
| Computer Code, Tutorial/ Problem Set | Assignment 1 | 14% |
31/03/2025 1:00 pm |
| Computer Code, Tutorial/ Problem Set | Assignment 2 | 14% |
28/04/2025 1:00 pm |
| Computer Code, Tutorial/ Problem Set | Assignment 3 | 14% |
26/05/2025 1:00 pm |
| Examination | Final Exam | 58% |
End of Semester Exam Period 7/06/2025 - 21/06/2025 |
Assessment details
Assignment 1
- Mode
- Written
- Category
- Computer Code, Tutorial/ Problem Set
- Weight
- 14%
- Due date
31/03/2025 1:00 pm
- Learning outcomes
- L01, L02, L03, L04, L05, L06
Task description
The assignment will contain practical problems, computer implementation of models, and theoretical components.
Submission guidelines
Upload via Blackboard: Please submit your written answers to all the assignment questions as one PDF document. If you need to add code please do so as separate clearly labelled files.
Deferral or extension
You may be able to apply for an extension.
The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.
A maximum of seven calendar days is allowed for an extension because the solutions need to be released.
See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.
Late submission
A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.
Assignment 2
- Mode
- Written
- Category
- Computer Code, Tutorial/ Problem Set
- Weight
- 14%
- Due date
28/04/2025 1:00 pm
- Learning outcomes
- L06, L07, L08, L09, L10, L11, L12
Task description
The assignment will contain practical problems, computer implementation of models, and theoretical components.
Submission guidelines
Upload via Blackboard: Please submit your written answers to all the assignment questions as one PDF document. If you need to add code please do so as separate clearly labelled files.
Deferral or extension
You may be able to apply for an extension.
The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.
A maximum of seven calendar days is allowed for an extension because the solutions need to be released.
See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.
Late submission
A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.
Assignment 3
- Mode
- Written
- Category
- Computer Code, Tutorial/ Problem Set
- Weight
- 14%
- Due date
26/05/2025 1:00 pm
- Learning outcomes
- L11, L12, L13, L14, L15, L16, L17, L18
Task description
The assignment will contain practical problems, computer implementation of models, and theoretical components.
Submission guidelines
Upload via Blackboard: Please submit your written answers to all the assignment questions as one PDF document. If you need to add code please do so as separate clearly labelled files.
Deferral or extension
You may be able to apply for an extension.
The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.
A maximum of seven calendar days is allowed for an extension because the solutions need to be released.
See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.
Late submission
A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.
Final Exam
- Mode
- Written
- Category
- Examination
- Weight
- 58%
- Due date
End of Semester Exam Period
7/06/2025 - 21/06/2025
- Learning outcomes
- L01, L02, L03, L04, L05, L06, L07, L08, L09, L10, L11, L12, L13, L14, L15, L16, L17, L18
Task description
The final examination will test all topics presented in the course.
The examination will be invigilated on-campus. One A4 sheet of handwritten notes, double-sided, is permitted. The approved calculator for the course is the Casio FX-82 (any model). You may use other calculators, but they must be labelled with an official 'Approved' sticker.
Further details will be provided to students before the examination period.
Exam details
| Planning time | 10 minutes |
|---|---|
| Duration | 120 minutes |
| Calculator options | (In person) Casio FX82 series only or UQ approved and labelled calculator |
| Open/closed book | Closed Book examination - specified written materials permitted |
| Materials | One A4 sheet of handwritten notes, double sided, is permitted |
| Exam platform | Paper based |
| Invigilation | Invigilated in person |
Submission guidelines
Deferral or extension
You may be able to defer this exam.
See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.
Course grading
Full criteria for each grade is available in the Assessment Procedure.
| Grade | Description |
|---|---|
| 1 (Low Fail) |
Absence of evidence of achievement of course learning outcomes. Course grade description: Student will achieve a final mark of at least 1% and less than 20% by demonstrating a poor knowledge/understandingﾠof the basic concepts in the course material. |
| 2 (Fail) |
Minimal evidence of achievement of course learning outcomes. Course grade description: Students must achieve a final mark of at least 20% and less than 45% by demonstrating some knowledge of the basic concepts of the course materials. This includes attempts at expressing their deductions and explanations as well as attempts to answer a few questions accurately. |
| 3 (Marginal Fail) |
Demonstrated evidence of developing achievement of course learning outcomes Course grade description: Students must achieve a final mark of at least 45% and less than 50% by demonstrating some knowledge of the basic concepts of financial mathematics as discussed in the course and its associated materials. This includes occasionally expressing their deductions and explanations clearly, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems. |
| 4 (Pass) |
Demonstrated evidence of functional achievement of course learning outcomes. Course grade description: Students must achieve a final mark of at least 50% and less than 65% by demonstrating an understanding of the basic concepts of financial mathematics as discussed in the course and its associated materials. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems and successfully applied this knowledge in some cases. |
| 5 (Credit) |
Demonstrated evidence of proficient achievement of course learning outcomes. Course grade description: Students must achieve a final mark of at least 65% and less than 75% by demonstrating an adequate understanding of the course theory as discussed in the course and its associated materials. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems and successfully applied this knowledge in several cases. |
| 6 (Distinction) |
Demonstrated evidence of advanced achievement of course learning outcomes. Course grade description: Students must achieve a final mark of at least 75% and less than 85% by demonstrating a comprehensive understanding of the theory of financial mathematics as discussed in the course and its associated materials. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification. |
| 7 (High Distinction) |
Demonstrated evidence of exceptional achievement of course learning outcomes. Course grade description: Students must achieve a final mark of at least 85% by demonstrating an excellent understanding of all the theory of financial mathematics as discussed in the course and its associated materials. This includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification. |
Additional course grading information
Hurdle: Students must achieve a mark of 40% or more on the final exam to pass the subject.
Supplementary assessment
Supplementary assessment is available for this course.
Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply.
Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.
If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.
Supplementary assessment in this course will be a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment.
Additional assessment information
Artificial Intelligence
Assessment tasks in this course evaluate students' abilities, skills and knowledge without the aid of generative Artificial Intelligence (AI) or Machine Translation (MT). Students are advised that the use of AI or MT technologies to develop responses is strictly prohibited and may constitute student misconduct under the Student Code of Conduct.
Applications for Extensions to Assessment Due Dates
Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.
Please note:
- Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
- Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
- If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
- If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
- If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
- For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
- Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
- If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
- There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.
Applications to defer an exam
In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.
Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.
Please note:
- Applications can be submitted no later than 5 calendar days after the date of the original exam.
- There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
- Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
- All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
- You’ll receive an email to your student email account when the status of your application is updated.
- If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.
Learning resources
You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.
Library resources
Find the required and recommended resources for this course on the UQ Library website.
Additional learning resources information
Students should regularly check theﾠBlackboard website https://learn.uq.edu.au/ for course materials and additional resources.
Learning activities
The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.
Filter activity type by
Please select
| Learning period | Activity type | Topic |
|---|---|---|
Multiple weeks From Week 1 To Week 13 |
Lecture |
Lecture series Introduce students to the basic tools and techniques of financial and actuarial mathematics. Learning outcomes: L01, L02, L03, L04, L05, L06, L07, L08, L09, L10, L11, L12, L13, L14, L15, L16, L17, L18 |
Multiple weeks From Week 2 To Week 13 |
Practical |
Exercises and Problems Contact with tutor for students to ask questions. Questions and problems for students to reinforce their understanding of the material. Learning outcomes: L01, L02, L03, L04, L05, L06, L07, L08, L09, L10, L11, L12, L13, L14, L15, L16, L17, L18 |
Policies and procedures
University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:
- Student Code of Conduct Policy
- Student Integrity and Misconduct Policy and Procedure
- Assessment Procedure
- Examinations Procedure
- Reasonable Adjustments - Students Policy and Procedure
Learn more about UQ policies on my.UQ and the Policy and Procedure Library.