2025/26 Undergraduate Module Catalogue

MATH2501 Financial Mathematics

20 Credits Class Size: 275

Module manager: Xiling Zhang
Email: x.zhang2@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2025/26

Pre-requisites

MATH1000 Core Mathematics
MATH1700 Probability and Statistics

Module replaces

MATH2535 and MATH2545

This module is not approved as a discovery module

Module summary

The module provides an introduction to diverse financial applications of mathematics. The different applications are considered within the three broad categories of risk management, insurance and financial liabilities and pricing of financial assets. This module serves as a first course in the pathway leading to potential careers in quantitative finance and actuarial disciplines.

Objectives

The module introduces a wide range of topics in financial mathematics (topics listed in syllabus below). The aim is to equip the students with basic knowledge in financial risk management and asset pricing, and most importantly how to model such problems in the mathematical language. This will be achieved by a structured series of lectures and consolidated by interactive tutorials. Students will also have hands-on practice during practicals where the knowledge acquired from lectures is implemented in Excel.

Learning outcomes

On successful completion of the module students will have demonstrated the following learning outcomes:

1. Model uncertain outcomes of financial investments, and make calculations based on those models.
2. Know different approaches to modelling of investor preferences and how they are used in portfolio optimisation.
3. Understand and apply quantitative risk management methods in financial applications.
4. Understand insurance claims management and risk of ruin.
5. Demonstrate familiarity with commonly used financial derivatives.
6. Understand and apply concepts of no-arbitrage pricing and replication of financial derivatives.
7. Apply and understand derivative pricing principles in a binomial model of financial markets.

Skills Learning Outcomes

On successful completion of the module students will have demonstrated the following skills learning outcomes:

a. Identify and set goals for studying the subject and a long-term career perspective.
b. Search for relevant literature and online resources to aid learning.
c. Communicate mathematical ideas and reasoning using written and spoken media.
d. Manage workload and deadlines through prioritisation and productivity skills.
e. Maintain and uphold academic integrity and professional ethics.
f. Use Excel to manipulate data and solve actuarial problems.

Syllabus

The module will cover the following topics:

1. Stochastic investment returns;
2. Investor preferences: Utility functions and expected utility; and Mean-variance portfolio theory and the Capital Asset Pricing Model.
3. Institutional risk management: Measures of risk, insurance claim management and ruin theory.
4. Forward contracts and model free arbitrage pricing using replication.
5. Financial derivatives, e.g., call/put options.
6. No arbitrage pricing in a single and multi-period binomial model: replication and risk-neutral pricing.

Methods of assessment
The assessment details for this module will be provided at the start of the academic year

Teaching Methods

Delivery type Number Length hours Student hours
Lecture 44 1 44
Practical 8 1 8
Seminar 10 1 10
Private study hours 138
Total Contact hours 62
Total hours (100hr per 10 credits) 200

Reading List

Check the module area in Minerva for your reading list

Last updated: 30/04/2025

Errors, omissions, failed links etc should be notified to the Catalogue Team