Module code: MATM067

Module Overview

Asset prices in financial markets go up and down in accordance with how markets digest the flow of information. To understand the causal relation between information flow and price movements, it is necessary to model market information and use this to infer the price dynamics. In this way, market dynamics can be replicated artificially on a computer. This module explains the powerful process of artificially generating realistic market models.


The module begins with elements of probability theory. We will then learn the idea of conditional expectation and the Bayes formula, which gives the optimal inference under uncertainty. The meaning of the Bayes formula will be explained, leading to the understanding of what is meant by “intelligence”.


The module then covers the basics of stochastic process (specifically, the Brownian motion) and calculus (specifically, the Ito calculus), sufficient to follow the contents of the module. Then simple models for flows of information in financial markets will be introduced, and by use of the Bayes formula the associated price dynamics will be derived.


The module concludes with a brief application to the asset valuation problems in financial markets (such as options or other derivatives). 

Module provider

Mathematics & Physics

Module Leader

BRODY Dorje (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 7

Module cap (Maximum number of students): N/A

Overall student workload

Independent Learning Hours: 52

Lecture Hours: 33

Guided Learning: 32

Captured Content: 33

Module Availability

Semester 1

Prerequisites / Co-requisites


Module content

Indicative content includes: measurable spaces; probability spaces; random variables; conditional probability; Bayes formula; artificial learning; Brownian motion; Ito calculus; simulating information-driven real-world phenomena; asset pricing; financial derivatives; valuation of credit-risky bonds

Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-Semester Test (1 hour, during the term, invigilated) 20
Examination Examination (2 hours, at the end of the term, invigilated) 80

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate


  • The ability to work out conditional probabilities;

  • The basic understanding of how to model the flow of information in an environment with uncertainties;

  • The ability to apply the modelling of information to deduce asset price dynamics;

  • The ability to price basic financial contracts using resulting models for the asset prices. 


Thus, the summative assessment for this module consists of:


  • One in-semester test, covering LO1 and LO3.

  • One examination, covering LO2, LO3, LO4, and LO5.


Formative assessment and feedback


There is feedback from coursework assignments. Verbal feedback is provided by the lecturer during the lectures (e.g., when exercises are worked out), and also in office hours.

Module aims

  • ¿ To equip students with the understanding of basic probability rules and the role of conditioning to navigate their way through the modelling of learning through uncertainties.
  • ¿ To equip students with the understanding of the modelling of information flow in financial markets and use this to deduce implied asset price processes.
  • ¿ To equip students with the basic understanding of the valuation of financial contracts.

Learning outcomes

Attributes Developed
001 Demonstrate working knowledge of probability spaces, probability measures, random variables, and their use in mathematical models for random events. K
002 Demonstrate working knowledge of applications of Brownian motion and other stochastic processes. K
003 Demonstrate a working knowledge of the Bayes formula and what is implied by the formula in cognitive science. K
004 Demonstrate skills in pricing financial derivatives. CPT
005 Demonstrate understanding the concept of synthetic data generation using artificial models. PT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to:


  • Offer an introduction to probability theory, with a focus on the role of conditioning and the Bayes formula, sufficient to model uncertain events.

  • Introduce the idea of modelling the flow of information, and how people’s perceptions change by digesting noisy information. 

  • Introduce how the flow of information will affect prices in financial markets.

  • Introduce the basics of product structures in financial market.

  • Demonstrate how asset price models can be used for the valuation of financial contracts. 


The learning and teaching methods include:


Weekly lectures during the term. Typeset notes, containing exercises and examples, will be provided along the way.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: MATM067

Other information

Resourcefulness and Resilience & Employability: This module teaches the basic mathematical skills required to model random events under uncertainties. This idea forms the foundation of many real-world applications, including the artificial intelligence. The module also introduces how such a skill can be used to deduce realistic models for asset prices in financial markets. This is used to explain how the valuation of financial contracts can be achieved. All of these contribute significantly towards enhancing resourcefulness, resilience, and employability of the students, owing in part to the fact that the techniques taught here can be applied to some of the new challenges in many industry applications in the uncertain world, most notably in the financial and insurance sectors.


Global and Cultural Intelligence: The modern approach taught in the module, based on research-led contents, and the knowledge on how investment banking world operates, are also beneficial towards enhancing global and cultural intelligence of the students.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 1 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 50% is required to pass the module
Financial Data Science MSc 1 Compulsory A weighted aggregate mark of 50% is required to pass the module
Mathematics MSc 1 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MPhys 1 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MMath 1 Optional A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.