Mathematical Methods of Finance - MAT00091M
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 2024-25 |
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:
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Use the language and tools of probability theory with confidence in the context of financial models and applications.
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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.
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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.
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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