# Module Directory

## MA126-4-SP-CO:Financial Mathematics

The details
2019/20
Mathematical Sciences
Colchester Campus
Spring
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019

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

MA211, MA212, MA311

## Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad)

## Module description

For students outside of the Department, an appropriate A level in Mathematics (or equivalent) is required for this module. If you are unsure whether you meet this criteria please contact mathsug@essex.ac.uk before attempting to enrol. This module provides a grounding in financial mathematics and its simple applications. This module covers Units 1, 2 & 3 of required material for the Institute and Faculty of Actuaries CM1 syllabus (Actuarial Mathematics, Core Principles).

## Module aims

Syllabus

i) generalised cashflow model to describe financial transactions
ii) take into account the time value of money using the concepts of compound
interest and discounting.
iii) Expressing interest rates and discount rates in terms of different time periods.
iv) Real and money interest rates.
v) Present value and accumulated value of a stream of payments
vi) Using compound interest functions including annuities certain.
vii) Equations of value.
viii) Loans repayments by instalments.
ix) Discounted cashflow techniques and investment project appraisal.
x) Investment and risk characteristics of assets such as fixed interest borrowings (government and others), shares, derivatives.
xi) Analysis of elementary compound interest problems.
xii) Delivery price and value of forward contracts.
xiii) Term structure of interest rates.
xiv) Simple stochastic models for investment returns.

## Module learning outcomes

On completion of this module, students should be able to: describe how to take into account the time value of money using the concepts of compound interest and discounting; show how interest rates or discount rates may be expressed in terms of different time periods; demonstrate a knowledge and understanding of real and money interest rates; calculate the present value and the accumulated value of a stream of payments using specified rates of interest, and the net present value at a real rate of interest; apply a generalised cash flow model to analyse financial transactions; derive and solve equations of value; show how discounted cash flow techniques can be used in measurement of investment project performance; derive formulae for different types of annuities; describe how a loan may be repaid by regular instalments of interest and capital; describe the investment and risk characteristics of typical assets available for investment purposes; analyse elementary compound interest problems allowing for both income tax and capital gains tax liabilities and calculate the real yield from the fixed-interest securities; show an understanding of the term structure of interest rates; evaluate the duration and convexity of a cash flow sequence, and their use in Redington immunisation of a portfolio of liabilities; define the concept of arbitrage, explain the significance of the no-arbitrage assumption and use this assumption to calculate the forward price of a number of derivative-type contracts; show an understanding of simple stochastic models for investment returns.

## Module information

Syllabus

1. The time value of money
1.1 Simple interest
1.2 Compound interest
1.3 Nominal and effective interest rates
1.4 The force of interest
1.5 Real and money interest rates
1.6 Discounting and accumulating

2. Cash flows and investment project appraisal
2.1 Cash flows and their value
2.2 Net present value and discounted cash flow
2.3 Equations of value
2.4 The internal rate of return
2.5 The comparison of two investment projects
2.6 Measurement of investment project performance

3. Annuities and loan schedules
3.1 Annuities
3.2 Perpetuities
3.3 Deferred Annuities
3.4 Varying annuities
3.5 Loan schedules

4. The valuation of securities
4.1 Fixed-interest securities
4.2 Related assets
4.3 Prices and yield
4.4 The effect of the term to redemption on the yield
4.5 Optional redemption dates
4.6 Real returns and index-linked securities

5. Capital Gains Tax
5.1 Fixed-interest securities and running yields
5.2 Income tax and capital gains tax
5.3 Offsetting capital losses against capital gains
5.4 Indexation of Capital Gains Tax

6. Term structures and immunization
6.1 Spot and forward rates
6.2 Duration
6.3 Convexity
6.4 Redington immunisation

7. Arbitrage and forward contracts
7.1 Arbitrage
7.2 Forwards contract
7.3 Calculating the forward price
7.4 Speculation, hedging, gearing (leverage)
7.5 The value of a forward contract prior to maturity

8. Stochastic interest rate models
8.1 Simple model
8.2 Independent annual rates of return
8.3 The log-normal distribution

## Learning and teaching methods

This module has 30 lectures and five lab classes in the spring term. There are three revision hours in the summer term.

## Bibliography

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Homework
Coursework   Test in PC Lab
Exam  1440 minutes during Summer (Main Period) (Main)

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Junlei Hu, email: j.hu@essex.ac.uk.
Dr Junlei Hu, email j.hu@essex.ac.uk
Dr Junlei Hu (j.hu@essex.ac.uk)

Availability
Yes
Yes
No

## External examiner

No external examiner information available for this module.
Resources
Available via Moodle
Of 114 hours, 35 (30.7%) hours available to students:
79 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information
Mathematical Sciences

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