# F78AB Actuarial and Financial Mathematics B

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

Aims:

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.

Summary:

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.

Syllabus:

• 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

• 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