F71AB Financial Mathematics

Dr Catherine Donnelly

Course co-ordinator(s): Dr Catherine Donnelly (Edinburgh).


This course aims to provide postgraduate students with a broad knowledge of basic concepts in financial mathematics including interest rates, arbitrage, stochastic interest rates, inflation and continuous cash flows.


  • Introduction
  • Rates of interest and discount
  • Present values, equations of values and yields
  • Annuities
  • Loan schedules
  • Project appraisal
  • The yield on a fund
  • Fixed interest securities
  • Index-linked securities
  • Forward contracts
  • The term structure of interest rates
  • Stochastic interest rate models

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisites: none.

Location: Edinburgh.

Semester: 1.

Learning Outcomes: Subject Mastery

At the end of studying this course, students should be able to:

  • Understand theory and practice of compound interest.
  • Know how to value and accumulate cash flows (e.g. which arise from commercial projects) and calculate internal rates of return.
  • Know the derivation of formulae for standardised cash flows (standard actuarial functions).
  • Derive and solve equations of value.
  • Understand theory and practice of loan repayments.
  • Understand the measure of investment performance.
  • Value fixed interest rate securities subject to tax and determine their yield.
  • Understand characteristics of ordinary shares, commercial property.
  • Calculate the delivery price and value of forward contracts using arbitrage free pricing.
  • Understand forward interest rates.
  • Understand the term structure of interest rates.
  • Calculate the duration and convexity of a set of cash flows.
  • Understand Redington’s theory of immunization.
  • Understand simple stochastic interest rate models.

Learning Outcomes: Personal Abilities

On completion of this course the student should be able to

  •  demonstrate knowledge and critical understanding of the basic concepts and models in financial mathematics.
  • demonstrate the ability to learn independently
  • manage time, work to deadlines and prioritize workloads
  • present results in a way that demonstrates that they have understood the technical and broader issues in financial mathematics

Reading list:

McCutcheon, J.J. & Scott, W.F. (1995): An Introduction to the Mathematics of Finance. Published for the Institute and the Faculty of Actuaries.

Formulae and Tables for Actuarial Examinations. Published for the Institute and the Faculty of Actuaries.

Hull, J. C. (2000): Options, Futures, and Other Derivatives. 4th ed. Prentice Hall.

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: 11.

Credits: 15.

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