Accessibility statement

Mathematical Finance in Discrete Time - MAT00096M

« Back to module search

• Department: Mathematics
• Module co-ordinator: Dr. Alex Daletskii
• Credit value: 20 credits
• Credit level: M
• Academic year of delivery: 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 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

• None

Prohibited combinations

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.

Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Mathematical Finance in Discrete Time
3 hours 80
Essay/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
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.