**Course co-ordinator(s):** Dr Brian Moretta (Edinburgh), Dr Karamjeet Singh (Malaysia).

**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

**Pre-requisites:** none.

**Location: **Edinburgh.

**Semester: **2.

**Learning Outcomes: Subject Mastery**

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

- Understand how an appropriate inflation index (such as the Retail Price Index) may be used to measure changes in the value of money with the passage of 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 what, in relation to a given inflation index, is meant by the `real yield’ for a particular investment and be able to calculate such yields
- Describe and calculate nominal rates of interest
- Value and accumulate continuously-payable cash flows and 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.
- 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.

**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:**

There will be a two-hour end-of-course examination, contributing 85% of the total mark. During the semester, there will be continuous assessment counting for 15% of the total mark.

**SCQF Level: **8.

## Other Information

**Help:** If you have any problems or questions
regarding the course, you are encouraged to contact the lecturer

**VISION:** further information and course materials
are available on VISION