F78AA Actuarial and Financial Mathematics A

Dr Karamjeet Singh

Course co-ordinator(s): Dr Karamjeet Singh (Malaysia), Peter Ridges (Edinburgh), Dr Haslifah Hasim (Dubai).

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.

 

Assessment Methods: Due to covid, assessment methods for Academic Year 2021/22 may vary from those noted on the official course descriptor. Please see:
- Maths (F1) Course Weightings 2021/22
- Computer Science (F2) Course Weightings 2021/22
- AMS (F7) Course Weightings 2021/22

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