MA226-5-AU-CO:
Financial Mathematics
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Current
Thursday 05 October 2023
Friday 15 December 2023
15
04 January 2024
Requisites for this module
(none)
(none)
(none)
(none)
(none)
BSC N233 Actuarial Science (Including Placement Year),
BSC N233DT Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DF Actuarial Science,
BSC N323DT Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
MSCIN399 Actuarial Science and Data Science,
BSC N333 Actuarial Studies,
BSC N333DT Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N334DT Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)
This module aims to provide a grounding in financial mathematics and its simple applications.
This module covers Units 1, 2 & 3 of CM1 of required material for the Institute and Faculty of Actuaries CM1 syllabus (Actuarial Mathematics, Core Principles).
The aims of this module are:
- Data and basics of modelling [CM1-1.1,1.2].
- The time value of money [CM1-2.1,2.2,2.3].
- Cash flows and investment project appraisal [CM1-1.3,3.1,3.3].
- Annuities and loan schedules [CM1-2.4,2.5,3.2].
- The valuation of securities [CM1-3.2].
- Capital Gain Tax [CM1-3.2].
- Term structures and immunisation [CM1-2.6,2.7].
By the end of this module, students will be expected to be able to:
- Have deep knowledge and critical understanding of the principles of actuarial modelling.
- Apply underlying concepts and principles of generalised cashflow models to describe financial transactions.
- Show how interest rates may be expressed in different time periods.
- Deep knowledge and critical understanding of real and money interest rates.
- Describe how to take into account time value of money using the concepts of compound interest and discounting.
- Apply underlying concepts and principles in order to calculate present value and accumulated value for a given stream of equal or unequal payments using specified rates of interest.
- Have deep knowledge, critical understanding and derivation of the compound interest functions (where payments can be in advance or in arrears).
- Have deep knowledge and critical understanding of the term structure of interest rates.
- Have deep knowledge and critical understanding of duration, convexity and immunisation of cashflows.
- Define an equation of value.
- Use the concept of equation of value to solve various practical problems.
- Apply underlying concepts and principles in order to show how discounted cashflow and equation of value techniques can be used in project appraisals.
- Gain deep knowledge and critical understanding of how to implement financial mathematics in Microsoft Excel spreadsheet and to become adept in using some of Excel's built-in financial and statistical functions and other useful tools.
Syllabus
- Data and basics of modelling [CM1-1.1,1.2]
- Introduction on data analysis.
- Actuarial modelling principles.
- The time value of money [CM1-2.1,2.2,2.3]
- Simple interest.
- Compound interest.
- Nominal and effective interest rates.
- The force of interest.
- Real and money interest rates.
- Discounting and accumulating.
- Applications in Excel.
- Cash flows and investment project appraisal [CM1-1.3,3.1,3.3]
- Cash flows and their value.
- Net present value and discounted cash flow.
- Equations of value.
- The internal rate of return.
- The comparison of two investment projects.
- Measurement of investment project performance.
- Applications in Excel.
- Annuities and loan schedules [CM1-2.4,2.5,3.2]
- Annuities.
- Perpetuities.
- Deferred Annuities.
- Varying annuities.
- Loan schedules.
- Applications in Excel.
- The valuation of securities [CM1-3.2]
- Fixed-interest securities.
- Related assets.
- Prices and yield.
- The effect of the term to redemption on the yield.
- Optional redemption dates.
- Real returns and index-linked securities.
- Applications in Excel.
- Capital Gain Tax [CM1-3.2]
- Fixed-interest securities and running yields.
- Income tax and capital gains tax.
- Offsetting capital losses against capital gains.
- Indexation of Capital Gains Tax.
- Inflation adjustments.
- Applications in Excel.
- Term structures and immunisation [CM1-2.6,2.7]
- Spot and forward rates.
- Duration.
- Convexity.
- Redington immunisation.
- Applications in Excel.
Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.
-
Garrett, S.J., McCutcheon, J.J. and W. F. Scott (2013)
An Introduction to the Mathematics of Finance: A Deterministic Approach. 2nd edn. Oxford, UK: Butterworth-Heinemann. Available at:
https://doi.org/10.1016/C2012-0-07620-X.
The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's
reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| Exam |
Main exam: In-Person, Open Book (Restricted), 180 minutes during Summer (Main Period)
|
| Exam |
Reassessment Main exam: In-Person, Open Book (Restricted), 180 minutes during September (Reassessment Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr John O'Hara, email: johara@essex.ac.uk.
Dr John O'Hara; Dr Terry Sithole
maths@essex.ac.uk
Yes
Yes
Yes
Available via Moodle
Of 37 hours, 35 (94.6%) hours available to students:
0 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.
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