Mathematical Finance in Discrete Time - MAT00088H
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, apply no-arbitrage principle for the valuation of derivative securities and use different compounding methods to compute streams of payments. 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 2025-26 |
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, apply no-arbitrage principle for the valuation of derivative securities and use different compounding methods to compute streams of payments. 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 basic compounding methods
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Describe, analyse, and apply the theory of arbitrage pricing in complete markets in discrete time
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.
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.
Shreve, S. (2004), Stochastic Calculus for Finance I: The binomial asset pricing model, Springer.