Module code: MAT3049

Module Overview

This module is an introduction to modern asset pricing theory.

The module begins with elements of stochastic calculus (specifically, the Ito calculus) sufficient to follow basic ideas in asset pricing theory that underlies modern investment banking.

After the introduction to background mathematics, the module develops the theory of asset pricing in an axiomatic way so as to avoid irrelevant digression and to get straight to the main idea of “pricing kernel” that lies at the heart of pricing financial contracts.

As a simple example, the Black-Scholes option pricing formula is derived.

The module then develops interest rate theory and introduces, as an example, the Vasicek model, but presented in the modern language using pricing kernel.

The module concludes with a brief application to modelling cryptocurrency economy.

Module provider


Module Leader

BRODY Dorje (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

JACs code: G120

Module cap (Maximum number of students): 83

Module Availability

Semester 1

Prerequisites / Co-requisites

MAT2003 Stochastic Processes

Module content

Indicative content includes: measurable spaces; σ-algebras; filtrations; probability spaces; random variables; martingales; supermartingales; submartingales; continuous-time stochastic processes; Brownian motion; stochastic integration; Ito calculus; pricing kernel; axiomatic approach to asset pricing; discount bonds; short rates; Libor and swap rates; interest rate derivatives; bond pricing formula; Vasicek model for short rates; bond pricing in the Vasicek model .

Assessment pattern

Assessment type Unit of assessment Weighting
Examination Examination 80
School-timetabled exam/test In-Semester Test 20

Alternative Assessment


Assessment Strategy

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

• The ability to manipulate stochastic processes;
• The basic knowledge of the subject, such as important definitions and concepts;
• The ability to combine theory with a model to arrive at prices of financial products.

Thus, the summative assessment for this module consists of:

• One two-hour examination at the end of Semester 1, worth 80% of the module mark;
• One in-semester test, worth 20% of the module mark.

Formative assessment and feedback:

There is feedback from unassessed 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 stochastic calculus sufficient to navigate their way through asset pricing theory.
  • To equip candidates with the understanding of the modern approach to asset pricing using pricing kernel.
  • To equip candidates with the understanding of interest rate modelling.

Learning outcomes

Attributes Developed
001 Demonstrate working knowledge of probability spaces, σ-algebras, 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 pricing kernel, and the distinction between pricing and hedging. K
004 Demonstrate skills in pricing financial derivatives. CPT
005 Demonstrate skills in pricing interest rate options and other financial products in the Vasicek model. CPT
006 Demonstrate understanding the differences between sovereign currency and cryptocurrency interest rates PT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Overall student workload

Independent Study Hours: 117

Lecture Hours: 33

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Offer a short introduction to stochastic calculus sufficient to perform stochastic differentiation / integration.
• Introduce the modern theory of asset pricing in the most direct and concise manner that is applicable to manage risks associated with a broad range of financial products.
• Demonstrate how well-known financial models like Black-Scholes and Vasicek can be worked out with little superfluous knowledge (such as risk-neutral valuation).

The learning and teaching methods include:

• 3 hour lectures per week, for 11 weeks. 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: MAT3049

Other information


Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% 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 2020/1 academic year.