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Mathematical Finance in Discrete Time - MAT00096M

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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

In this module you will learn the basic mathematics that is applied in the area of finance. In particular, you will learn how to build a theory of portfolio selection and, consequently, asset prices in both complete and incomplete markets. This theory will then be applied to the valuation of financial and real assets. All models will be in discrete time.

Professional requirements

Counts towards IFoA exemption.

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

Post requisite module: Mathematical Finance in Continuous Time

Module will run

Occurrence Teaching period
A Semester 1 2023-24

Module aims

In this module you will learn the basic mathematics that is applied in the area of finance. In particular, you will learn how to build a theory of portfolio selection and, consequently, asset prices in both complete and incomplete markets. This theory will then be applied to the valuation of financial and real assets. All models will be in discrete time.

Module learning outcomes

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

  1. Describe, analyse, and apply the Markowitz portfolio theory

  2. Describe, analyse, and apply the Capital Asset Pricing Model

  3. Describe, analyse, and apply the theory of expected utility

  4. Describe, analyse, and apply the theory of arbitrage pricing in complete markets in discrete time

  5. (M-level only) Describe and analyse incomplete markets on example of the trinomial model.

Module content

The module starts by building a two-period model of financial markets that is used to explore the classical theory of portfolio selection due to Markowitz. This theory is then extended to a theory of asset prices (CAPM) in financial markets. In the context of the multi-period binomial model, you will learn about the no-arbitrage principle and how it can be used to price a variety of assets in a complete market, such as European, American and real options. We finish by discussing some well-known and oft-used risk measures.

The additional M-level material will be self-study, based on lecture notes and pre-recorded videos.

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 80
Essay/coursework 20

Special assessment rules

None

Additional assessment information

If a student has a failing module mark, only failed components need be reassessed.

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 80
Essay/coursework 20

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

Capinski, M. and T. Zastawniak (2003), Mathematics for Finance, Springer Verlag.

Evstigneev, I., T. Hens, and K. Schenk-Hoppé (2015), Mathematical Financial Economics, Springer Verlag.

Magill, M. and M. Quinzii (1996), Theory of Incomplete Markets, MIT Press.

Shreve, S. (2004), Stochastic Calculus for Finance I: The binomial asset pricing model, Springer.


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.