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Mathematical Methods of Finance (Online Version) - MAT00027M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Tomasz Zastawniak
  • Credit value: 20 credits
  • Credit level: M
  • Academic year of delivery: 2023-24

Module will run

Occurrence Teaching period
A1 Semester 1 2023-24
A2 Semester 1 2023-24 to Semester 2 2023-24
B1 Semester 2 2023-24
B2 Semester 2 2023-24 to Semester 1 2024-25

Module aims

This module provides the mathematical foundations underpinning Mathematical Finance. The topics covered are selected because of their importance in quantitative finance theory and practice. Probability theory and stochastic processes provide the language in which to express and solve mathematical problems in finance due to the inherent randomness of asset prices. The introduction of more advanced tools will be preceded by a brief review of basic probability theory with particular focus on conditional expectation. Then the module will proceed to present the theory of martingales and the study of three basic stochastic processes in finance: random walks, Brownian motion, and the Poisson process. An informal overview of Ito stochastic calculus will be given and first financial applications indicated. The material will be illustrated by numerous examples and computer-generated demonstrations. By the end of this module students are expected to achieve a sufficient level of competence in selected mathematical methods and techniques to facilitate further study of Mathematical Finance.

Module learning outcomes

By the end of this module students should

  • use the language and tools of probability theory with confidence in the context of financial models and applications;
  • acquire an understanding of stochastic processes in discrete and continuous time and be familiar with the basic examples and properties of such processes appearing in financial modelling;
  • recognise the central role of Ito stochastic calculus for mathematical models in finance, and show familiarity with the basic notions and tools of stochastic calculus, at an informal level.


Task Length % of module mark
Coursework - extensions not feasible/practicable
Coursework Assignment
N/A 100
Oral presentation/seminar/exam
Online Viva
N/A 0

Special assessment rules



Task Length % of module mark
Coursework - extensions not feasible/practicable
Coursework Assignment
N/A 100
Oral presentation/seminar/exam
Online Viva
N/A 0

Module feedback

Information currently unavailable

Indicative reading

1. M. Capinski and E. Kopp, Measure, Integral and Probability, 2nd edition, Springer 2007.
2. E. Kopp, J. Malczak and T. Zastawniak, Probability for Finance, Cambridge University Press 2014 (to appear).
3. M. Capinski and T. Zastawniak, Probability Through Problems, Springer 2001.
4. M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, Springer 2003.
5. Z. Brzezniak and T. Zastawniak, Basic Stochastic Processes, Springer 1999

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.