Mathematical Finance

About

This module provides a fundamental overview of mathematical finance. It begins with an overview of financial contracts, interest rates and the value of money. In particular, it discusses what constitutes a fair price for a contract and explains why fair prices are rarely used in everyday transactions.

You will then investigate financial markets in a discrete-time setting, with some revision of basic probability theory. The concept of risk-neutral asset pricing will be discussed with reference to pricing stocks and options in the exchange.

The final part of the module introduces key concepts of stochastic calculus and focuses on continuous-time finance through the widely used Black–Scholes model.

The aim is to give you a broad understanding of the application of finance theory while providing a strong theoretical foundation. It is also useful if you wish to explore the field and related industries before committing to a Mathematical Finance pathway or MSc, or as preparation for other undergraduate mathematical finance modules.

Week one: Introduction to Financial Markets and Financial Contracts
Value of money
Basic investment strategies
Put–call parity
No-arbitrage principle

Week two: Risk-neutral Asset Pricing
Risk-neutral measure
Contingent claims
One-period market
Risk-free portfolio
Multi-period model

Week three: Stochastic Analysis
Continuous-time limit of the multi-period model
Brownian motion
Stochastic integration
Black–Scholes model

Course leader

Dr Chak Hei Lo

Course aim

This module aims to:

- Introduce mathematical finance and give you a strong theoretical basis in finance theory as well as a comprehensive grasp of its applications.
- Provide a foundation and first steps towards pursuing a specialisation in the finance sector.
- Support those who wish to work in quantitative analysis and follow related career pathways.
- Serve as a foundation for other undergraduate mathematical‑finance courses or for individuals who wish to learn more about the area and associated sectors before committing fully to a mathematical finance route or an MSc in the subject

Fee info