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ACTL2111 Financial Mathematics for Actuaries
Course Details & Outcomes
Course Description
This course develops the financial mathematics required for the analysis of financial and insurance transactions. Topics covered include: mathematics of compound interest; valuation of cash flows of simple insurance contracts; analysis and valuation of annuities, bonds, loans and other securities; yield curves and immunisation; introduction to stochastic interest rate models and actuarial applications.
Course Learning Outcomes
Course Learning Outcomes | Program learning outcomes |
---|---|
CLO1 : Understand the concept of time value of money |
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CLO2 : Explain and compare different types of interest: simple vs compound interest, discount interest, nominal vs effective interest rates, rate vs force of interest, real vs money interest rates, the term structure of interest, as well as simple stochastic interest models |
|
CLO3 : Understand the relation between a present value, a set of cash flows and interest, as well as understand the interest rate risk (duration, immunisation) confidently the calculations and concepts learnt and applied in practical situations |
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CLO4 : Explain how to modify a simple valuation problem by taking into account tax and transaction costs |
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CLO5 : Assess financial calculations for reasonableness and criticise their assumptions |
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CLO6 : Describe, compare and value the following securities: bonds, shares, loans, forwards and futures contracts, options, annuities and life insurance contracts |
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CLO7 : Describe the basic market conventions in the securities and money markets for the instruments introduced during the course |
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CLO8 : Develop formulae for the expected value and variance of the present values of simple insurance and annuity contracts, assuming constant deterministic interest |
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CLO9 : Integrate financial valuation concepts to practical situations such as in investment project appraisals or in financial markets |
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CLO10 : Explain difficult concepts in simple terms and in an effective way, both in oral and written forms. |
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Course Learning Outcomes | Assessment Item |
---|---|
CLO1 : Understand the concept of time value of money |
|
CLO2 : Explain and compare different types of interest: simple vs compound interest, discount interest, nominal vs effective interest rates, rate vs force of interest, real vs money interest rates, the term structure of interest, as well as simple stochastic interest models |
|
CLO3 : Understand the relation between a present value, a set of cash flows and interest, as well as understand the interest rate risk (duration, immunisation) confidently the calculations and concepts learnt and applied in practical situations |
|
CLO4 : Explain how to modify a simple valuation problem by taking into account tax and transaction costs |
|
CLO5 : Assess financial calculations for reasonableness and criticise their assumptions |
|
CLO6 : Describe, compare and value the following securities: bonds, shares, loans, forwards and futures contracts, options, annuities and life insurance contracts |
|
CLO7 : Describe the basic market conventions in the securities and money markets for the instruments introduced during the course |
|
CLO8 : Develop formulae for the expected value and variance of the present values of simple insurance and annuity contracts, assuming constant deterministic interest |
|
CLO9 : Integrate financial valuation concepts to practical situations such as in investment project appraisals or in financial markets |
|
CLO10 : Explain difficult concepts in simple terms and in an effective way, both in oral and written forms. |
|
Learning and Teaching Technologies
Moodle - Learning Management System | Echo 360 | Zoom | EdStem
Learning and Teaching in this course
The approach adopted in this course is one of assisted self-study. While reading this subsection, please refer to the detailed course schedule.
Course materials are broadly organised in 7 categories. They consist of:
- Overview videos/ videos on common mistakes for each module
- Lecture recordings (available after each in-person lecture)
- Fully annotated lecture slides (available after each in-person lecture)
- Prescribed/reference books
- Exercises with solutions
- Selected past quizzes and exams for advanced exercises
- Downloadable "R tutorials" (platform for students to use R to solve problems)
Assessments
Assessment Structure
Assessment Item | Weight | Relevant Dates | Program learning outcomes |
---|---|---|---|
Quiz
Assessment FormatIndividual
|
15% |
|
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Assignment
Assessment FormatIndividual
|
25% |
|
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Final Examination
Assessment FormatIndividual
|
60% |
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Assessment Details
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Quiz
Assessment Overview
There will be two online quizzes (7.5% each). Each quiz will take about one hour to complete, and students will be given a 3-day window to work on the quiz. Full credit will be awarded based on a genuine attempt.
Assesses: PLO1, PLO2, PLO3Course Learning Outcomes
- CLO1 : Understand the concept of time value of money
- CLO2 : Explain and compare different types of interest: simple vs compound interest, discount interest, nominal vs effective interest rates, rate vs force of interest, real vs money interest rates, the term structure of interest, as well as simple stochastic interest models
- CLO3 : Understand the relation between a present value, a set of cash flows and interest, as well as understand the interest rate risk (duration, immunisation) confidently the calculations and concepts learnt and applied in practical situations
- CLO4 : Explain how to modify a simple valuation problem by taking into account tax and transaction costs
- CLO6 : Describe, compare and value the following securities: bonds, shares, loans, forwards and futures contracts, options, annuities and life insurance contracts
- CLO8 : Develop formulae for the expected value and variance of the present values of simple insurance and annuity contracts, assuming constant deterministic interest
- CLO9 : Integrate financial valuation concepts to practical situations such as in investment project appraisals or in financial markets
Detailed Assessment Description
The quiz will take place online on Moodle and can be taken at home or any place with an internet connection.
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Assignment
Assessment Overview
This is an Excel-based assignment for students to apply the theory learnt from lectures together with the Excel skills learnt from the lab sessions. Students will be given at least 2 weeks to complete the assignment.
Assesses: PLO1, PLO2, PLO3Course Learning Outcomes
- CLO9 : Integrate financial valuation concepts to practical situations such as in investment project appraisals or in financial markets
- CLO10 : Explain difficult concepts in simple terms and in an effective way, both in oral and written forms.
Detailed Assessment Description
The practical application of the course concepts based on actual financial problems is an important graduate attribute that employers require and this course aims to provide at least some introductory exposure to this. Writing skills for technical material are also important.
The assignment will assess application of Excel concepts to solving real life financial mathematics problems. This will provide students with an opportunity to develop communication and computational skills. It offers students the opportunity to engage in independent research, engage in critical analysis, and problem solving, as well as to demonstrate their understanding of the concepts and perspectives that are central to actuarial studies. The assignment will be made available at least two weeks before the due date, and students need to complete the assignment by submitting a single Excel document.
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Final Examination
Assessment Overview
This is a 2-hour closed book exam that will be invigilated and scheduled during the university exam period.
Assesses: PLO1, PLO2, PLO3Course Learning Outcomes
- CLO1 : Understand the concept of time value of money
- CLO2 : Explain and compare different types of interest: simple vs compound interest, discount interest, nominal vs effective interest rates, rate vs force of interest, real vs money interest rates, the term structure of interest, as well as simple stochastic interest models
- CLO3 : Understand the relation between a present value, a set of cash flows and interest, as well as understand the interest rate risk (duration, immunisation) confidently the calculations and concepts learnt and applied in practical situations
- CLO4 : Explain how to modify a simple valuation problem by taking into account tax and transaction costs
- CLO5 : Assess financial calculations for reasonableness and criticise their assumptions
- CLO6 : Describe, compare and value the following securities: bonds, shares, loans, forwards and futures contracts, options, annuities and life insurance contracts
- CLO7 : Describe the basic market conventions in the securities and money markets for the instruments introduced during the course
- CLO8 : Develop formulae for the expected value and variance of the present values of simple insurance and annuity contracts, assuming constant deterministic interest
- CLO9 : Integrate financial valuation concepts to practical situations such as in investment project appraisals or in financial markets
- CLO10 : Explain difficult concepts in simple terms and in an effective way, both in oral and written forms.
Detailed Assessment Description
The final exam will assess students’ understanding of the concepts covered in the course and their ability to apply them to financial market problems. A deeper grasp of materials is expected from students at the final exam level.
The final exam will take place on campus and will last for 2 hours on a date scheduled by the university. The final exam will be a closed book invigilated exam, and students will only be allowed to use the text "Formulae and Tables for Actuarial Examinations" into the exam. This must not be annotated.
General Assessment Information
Grading Basis
Standard
Requirements to pass course
A student is required to achieve 50% to pass the course.
Course Schedule
Teaching Week/Module | Activity Type | Content |
---|---|---|
Week 1 : 27 May - 2 June | Lecture |
Module 1 (Time Value of Money and Valuation of Cash Flows) |
Week 2 : 3 June - 9 June | Lecture |
Module 1 (Time Value of Money and Valuation of Cash Flows) |
Week 3 : 10 June - 16 June | Lecture |
Module 1 (Time Value of Money and Valuation of Cash Flows) |
Week 4 : 17 June - 23 June | Lecture |
Module 1 (Time Value of Money and Valuation of Cash Flows) Module 2 (Modelling Loans and Repayments) |
Week 5 : 24 June - 30 June | Lecture |
Module 2 (Modelling Loans and Repayments) |
Assessment |
Online quiz 1 |
|
Week 7 : 8 July - 14 July | Lecture |
Module 2 (Modelling Loans and Repayments) Module 3 (Interest Rate Risk) |
Week 8 : 15 July - 21 July | Lecture |
Module 3 (Interest Rate Risk) Module 4 (Derivatives) |
Assessment |
Assignment due (tentative) |
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Week 9 : 22 July - 28 July | Lecture |
Module 4 (Derivatives) |
Week 10 : 29 July - 4 August | Lecture |
Module 4 (Derivatives) Module 5 (Stochastic Returns) |
Attendance Requirements
Students are strongly encouraged to attend all classes and review lecture recordings.
Course Resources
Prescribed Resources
The required textbooks for the course are:
- Broverman, S.A. (2015/2017), Mathematics of Investment and Credit, 6th/7th Edition, ACTEX Publications. [A solutions manual is available for purchase. The 5th Edition is still largely similar to the 6th and 7th Editions, so it is possible to learn with the 5th Edition as well. However, the 4th, 3rd and 2nd Editions are not recommended.]
- Sherris, M. (1996), Money and Capital Markets, Pricing, Yields and Analysis, 2nd Edition, Allen & Unwin.
Additional (optional) readings are:
- Daniel, J. W. and Vaaler, L. J. F. (2007), Mathematical Interest Theory, Pearson, Prentice Hall. [A book similar to Brovermans, useful as a second reference if a second, different explanation is necessary. It also has the advantage of discussing the use of modern calculators and explaining how to use them.]
- Boyle, P.P., Cox, S.H., Dufresne, D., Gerber, H.U., Mueller, H.H., Pedersen, H.W., Pliska, S.R., Sherris, M., Shiu, E.S., Tan, K.S. (2001) Financial Economics: With Applications to Investments, Insurance and Pensions, Harry H. Panjer Ed., The Actuarial Foundation, Schaumburg, Illinois. [An advanced textbook, perhaps a bit too advanced for the level of the course.]
- Gerber, H.U. (1997), Life Insurance Mathematics, Springer-Verlag, 3rd Edition. [The absolute classic in Life Insurance Mathematics. Useful as an extremely concise optional reading. A new edition is not likely to appear in a near future.]
- Bowers, N.L. Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1997), Actuarial Mathematics, Society of Actuaries, 2nd Edition. [Another classic useful reference; a new edition is not likely to appear in a near future.]
All these books are available from the library, some of them with copies in the reserve.
Formulae & TablesFor closed book exams, students will only be allowed to bring into the examinations for the Actuarial courses in the Bachelor of Actuarial programme the text "Formulae and Tables for Actuarial Examinations". This text must not be annotated. All students in the actuarial courses should purchase a copy of this text if they wish to use this in the final examinations for this course. The text is available from the UNSW Bookshop or the UK Institute of Actuaries.
Course websiteThe course Moodle website is available from the UNSW TELT platform.
To access the Moodle online support site for students, follow the links from that website to UNSW Moodle Support/Support for Students. Additional technical support can be obtained from [email protected] (02 9385 1333).
All course contents will be available from the course website. It is essential that you visit the site regularly (at least once in two days) to see any announcements posted there by the course coordinator, as it will be assumed that they are known to you within a reasonable time.
Course Evaluation and Development
Feedback is regularly sought from students and continual improvements are made based on this feedback. At the end of this course, you will be asked to complete the myExperience survey, which provides a key source of student evaluative feedback. Your input into this quality enhancement process is extremely valuable in assisting us to meet the needs of our students and provide an effective and enriching learning experience. The results of all surveys are carefully considered and do lead to action towards enhancing educational quality.
Each course in actuarial studies at UNSW is reviewed each session by the course co-ordinator using student evaluative feedback from myExperience. Student feedback is taken seriously, and continual improvements are made to the course based on such feedback. Significant changes to the course are communicated to students taking the course. Your input into improving future offerings of the course is highly valued.
Some of the additional developments have been effected in recent years include:
- Replacement of an invigilated mid-term exam by two formative online quizzes;
- Corrections of typos in the exercises and improvement of the solutions;
- Enhancement of Excel lab materials;
- Removal of the module on life contingencies;
- Preparation of online videos to give student an overview (pre-module) on each module and some explanations on common mistakes/misconception (post-module);
- Development of "R tutorials" for students to learn to use R to solve practical problems related to the course.
- Reduction of assessment weight on the final exam.
We repeat that we take students’ feedback extremely seriously and we count on your cooperation when seeking feedback that will help us identify the strengths and weaknesses of the course contents and learning and teaching strategies. We guarantee that the process is entirely anonymous and that your feedback will not have any impact on your final results.