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# Mathematical Finance in Discrete Time - MAT00088H

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• Department: Mathematics
• Module co-ordinator: Dr. Alex Daletskii
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2024-25
• See module specification for other years: 2023-24

## 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

• None

### Prohibited combinations

Post requisite module: Mathematical Finance in Continuous Time

## Module will run

Occurrence Teaching period
A Semester 1 2024-25

## 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:

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

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

3. Describe, analyse and apply basic compounding methods

4. 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.

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Mathematical Finance in Discrete Time
3 hours 80
Essay/coursework
Coursework : Excel-based assignment
N/A 20

### Special assessment rules

None

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

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Mathematical Finance in Discrete Time
3 hours 80
Essay/coursework
Coursework : Excel-based assignment
N/A 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.

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 is constantly exploring 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 by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.