Course co-ordinator(s): Dr Alistair Wallis (Edinburgh), Dr Karamjeet Singh (Malaysia), Andres Barajas Paz (Edinburgh).
Aims:
To introduce the student to simple mathematical models of cashflows accumulated or discounted at interest, and to develop skill in applying these models to real financial contracts and transactions
Summary:
- Simple interest
- Compound interest and discount
- Time units and effective rates of interest
- Accumulations and present values of discrete-time cashflows
- Varying rates of interest
- Annuities
- Yields
- Measuring rates of return
- Loan schedules
- Fixed-interest securities
- Discounted Cash Flows
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Linked course(s): F78AB Actuarial and Financial Mathematics B .
Location: Edinburgh, Malaysia.
Semester: 1.
Syllabus:
- Simple interest
- Compound interest and discount
- Time units and effective rates of interest
- Accumulations and present values of discrete-time cashflows
- Varying rates of interest
- Annuities
- Yields
- Measuring rates of return
- Loan schedules
- Fixed-interest securities
- Discounted Cash Flows
- Stochastic interest rate models
- Inflation indexing and index-linked bond
Learning Outcomes: Subject Mastery
On completion of this course the student should be able to:
- Describe the basic concepts of simple and compound interest.
- Calculate the present value or accumulation of any set of discrete-time cashflows, at constant or varying rates of interest.
- Derive and use simple formulae for values of level and increasing annuities-certain.
- Explain the concept of the yield on a series of cashflows, and its limitations.
- Calculate time-weighted, money-weighted and internal linked rates of return.
- Analyse loan schedules, including simple alterations.
- Describe basic fixed-interest securities, and calculate prices and yields allowing for tax..
- Understand the discounted cash flow model and know what are internal rates of return (IRR), net present values (NPV) and break-even durations.
- Explain the concept of a stochastic interest rate model.
- Calculate the mean value and the variance of the accumulated amount of a single premium for a stochastic interest rate model in which the annual rates of return are independently and identically distributed (and also do this for other simple models).
- Calculate the mean value and the variance of the accumulated amount of a level annual premium for a stochastic interest rate model in which the annual rates of return are independently and identically distributed.
- Understand how an appropriate inflation index (such as the RPI) may be used to measure changes in the value of money with time.
- Understand how an appropriate index may be used to increase the monetary amounts of the future cash flows associated with a given `index-linked' investment and, in particular, how the RPI is used to determine the future payments of interest and capital associated with index-linked government securities.
- Know, in relation to a given inflation index, what is meant by the `real yield' for a particular investment and be able to calculate such yields.
- Use an appropriate computer package to apply the methods introduced in this course.
Learning Outcomes: Personal Abilities
- Interpreting problems from commercial practice in terms of relevant mathematical models
- Independently recognizing and applying appropriate mathematical techniques to solve problems
- Interpreting solutions expressed mathematically in terms of the original problem
- Communicating the solutions to complex problems in the financial services sector
Reading list:
- Garrett, S.J. (2013). An Introduction to the Mathematics of Finance (second edition). Butterworth-Heinemann.
- Zima, P. & Brown, R.L. (1996). Schaum’s Outline: Mathematics of Finance (Second Edition), McGraw Hill.
SCQF Level: 8.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas