F78AB Actuarial and Financial Mathematics B

Dr Karamjeet SinghDr Ayse Arik

Course co-ordinator(s): Dr Karamjeet Singh (Malaysia), Dr Ayse Arik (Edinburgh).


To introduce the student to more advanced mathematical models of cashflows accumulated or discounted at interest, and to develop skill in applying these models to real financial contracts and transactions.


This course builds on and extends the ideas contained in the related course F78AA Actuarial and Financial Mathematics A.

The concepts of a continuously-payable cashflow and the force of interest are considered, leading to a wider discussion of what is called the term-structure of interest rates and the yield curve.

The idea of indexing of cashflows, for example using a consumer price index, is introduced. This idea is applied to the valuation of index-linked securities.

Rates of return can be random and we see how to model and measure this risk. We see how interest-rate risk can be managed through the use of Redington’s immunisation theory. We understand and apply the no-arbitrage principle to price forward contracts.

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisites: none.

Linked course(s): F78AA Actuarial and Financial Mathematics A .

Location: Edinburgh, Malaysia.

Semester: 2.


  • Nominal rates of interest
  • Force of interest and continuous cash flows
  • Duration and Redington's theory of immunization
  • The term structure of interest rates
  • Forward contracts

Learning Outcomes: Subject Mastery

On completion of this course the student should be able to:

  • Describe and calculate nominal rates of interest.
  • Know how to value and accumulate continuously-payable cash flows and how to calculate internal rates of return for transactions with such cash flows.
  • Define the duration and convexity of a cash flow sequence and illustrate how these may be used to estimate the sensitivity of the value of the cash flow sequence to changes in the rate of interest.
  • Know how duration and convexity are used in the immunisation of a portfolio of liabilities.
  • Show an understanding of the term structure of interest rates and of the main factors influencing this structure.
  • Calculate the delivery price and the value of a forward contract, using arbitrage-free pricing methods and to explain what is meant by hedging in the case of a forward contract.
  • Know how to calculate the value of various types of forward contracts at any time during their duration.
  • 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: A Deterministic Approach. Oxford: Butterworth-Heinemann/Elsevier.
  • Formulae and Tables for Actuarial Examinations (“Yellow Tables”). Published for the Institute and the Faculty of Actuaries.

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.

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