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Mathematical Methods of Finance - MAT00091M

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  • Department: Mathematics
  • Credit value: 20 credits
  • Credit level: M
  • Academic year of delivery: 2023-24
    • See module specification for other years: 2024-25

Module summary

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 topics covered in this module are selected because of their importance in quantitative finance theory and practice.

Module will run

Occurrence Teaching period
A Semester 1 2023-24

Module aims

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 topics covered in this module are selected because of their importance in quantitative finance theory and practice.

Module learning outcomes

By the end of the module, students will be able to:

  1. Use the language and tools of probability theory with confidence in the context of financial models and applications.

  2. Demonstrate an understanding of stochastic processes in discrete and continuous time, in particular through the basic examples and properties of such processes appearing in financial modelling.

  3. Apply Ito stochastic calculus to mathematical models in finance, by working with examples of the basic notions and tools of stochastic calculus at an informal level.

  4. Work with the key notions and properties of martingale theory, and in particular its applications in stochastic calculus and relevance in quantitative finance.

Module content

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. A brief review of basic probability theory with particular focus on conditional expectation leads into the discussion of more advanced tools. Then the module will proceed to present the theory of martingales and the study of two basic stochastic processes in finance: random walks and Brownian motion. An informal overview of Ito stochastic calculus will be given and first financial applications indicated. 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.

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Special assessment rules

None

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

P. E. Kopp and T. Zastawniak, Probability for Finance, Cambridge, 2013.

M. Capinski, P. E. Kopp J. Traple, Stochastic Calculus for Finance, Cambridge, 2012.

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 constantly explores 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. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.