Mathematical Methods of Finance (Online Version) - MAT00027M

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Module will run

Occurrence	Teaching period
A1	Autumn Term 2022-23 to Spring Term 2022-23
A2	Autumn Term 2022-23 to Summer Term 2022-23
B1	Spring Term 2022-23 to Summer Term 2022-23
B2	Spring Term 2022-23 to Spring Term 2023-24

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.

Indicative assessment

Task	% of module mark
Coursework - extensions not feasible/practicable	100
Oral presentation/seminar/exam	0

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Coursework - extensions not feasible/practicable	100
Oral presentation/seminar/exam	0

Module feedback

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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