**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

**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