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.
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.
- 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.
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.
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