## MA226-5-AU-CO:Financial Mathematics

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Current
Thursday 03 October 2024
Friday 13 December 2024
15
22 April 2024

Requisites for this module
(none)
(none)
(none)
(none)

MA311

## Key module for

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),
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)

## Module description

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).

## Module aims

The aims of this module are:

• To introduce the basics of actuarial modelling centred on deterministic models and their applications to financial problems.

• To introduce the theory of interest and the consideration of cashflow models, investment decisions, annuities and their applications.

• To introduce the Capital Gains Tax and the term structure of bonds.

## Module learning outcomes

By the end of this module, students will be expected to be able to:

1. Have deep knowledge and critical understanding of the principles of actuarial modelling.

2. Apply underlying concepts and principles of generalised cashflow models to describe financial transactions.

3. Show how interest rates may be expressed in different time periods.

4. Deep knowledge and critical understanding of real and money interest rates.

5. Describe how to take into account time value of money using the concepts of compound interest and discounting.

6. 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.

7. Have deep knowledge, critical understanding and derivation of the compound interest functions (where payments can be in advance or in arrears).

8. Have deep knowledge and critical understanding of the term structure of interest rates.

9. Have deep knowledge and critical understanding of duration, convexity and immunisation of cashflows.

10. Define an equation of value.

11. Use the concept of equation of value to solve various practical problems.

12. Apply underlying concepts and principles in order to show how discounted cashflow and equation of value techniques can be used in project appraisals.

13. 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.

## Module information

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.

• Applications in Excel.

• Term structures and immunisation [CM1-2.6,2.7]

• Spot and forward rates.

• Duration.

• Convexity.

• Redington immunisation.

• Applications in Excel.

## Learning and teaching methods

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.

## Bibliography*

This module does not appear to have a published bibliography for this year.

## 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.

Coursework Exam
30% 70%

### Reassessment

Coursework Exam
30% 70%
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

Availability
Yes
Yes
Yes

## External examiner

Dr Melania Nica
Resources
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.

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements, industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules. The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.

The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.