Mathematical Finance in Discrete Time - MAT00096M
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
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:
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Describe, analyse, and apply the Markowitz portfolio theory
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Describe, analyse, and apply the Capital Asset Pricing Model
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Describe, analyse, and apply the theory of expected utility
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Describe, analyse, and apply the theory of arbitrage pricing in complete markets in discrete time
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(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.