Bachelor of Science (BSc)

BSc Computer Science and Mathematics with Industrial Experience

Graduate this highly sought-after subject combination having already gained invaluable experience in industry.
  • Duration: 4 years
  • Year of entry: 2025
  • UCAS course code: GG41 / Institution code: M20
  • Key features:
  • Industrial experience
  • Scholarships available

Full entry requirementsHow to apply

Fees and funding

Fees

Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £36,000 per annum. For general information please see the undergraduate finance pages.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Scholarships/sponsorships

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our  undergraduate student finance pages .

Course unit details:
Mathematical Modelling in Finance

Course unit fact file
Unit code MATH39032
Credit rating 10
Unit level Level 3
Teaching period(s) Semester 2
Available as a free choice unit? No

Overview

This course unit is primarily concerned with the valuation of financial instruments known as derivatives. To achieve this, a mathematical model is developed and then solved for different types of problems. It is assumed that students will be familiar with financial terms, stochastic differential equations, and partial differential equations. It is shown that mathematical methods developed to solve Partial Differential Equations can be powerful tools in solving financial problems once suitable models have been devised.

Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics of Waves and Fields PHYS20171 Pre-Requisite Optional
Introduction to Financial Mathematics MATH20912 Pre-Requisite Compulsory
Partial Differential Equations & Vector Calculus MATH24420 Pre-Requisite Compulsory
math39032 pre reqs

PHYS20171 is an acceptable alternative for those Maths-Physics students who took that unit instead of MATH24420

Aims

The unit aims to give students an insight into both the development and solution of the mathematical models used to describe the value of financial derivatives. As a result they should be able to both derive and solve for basic financial derivatives contracts.

Learning outcomes

On successful completion of the course, students will be able to:

1. Recognise the role that financial derivatives play in reducing risk

2. Derive boundary conditions for financial contracts priced under the Black-Scholes model

3. Construct a PDE to price financial contracts, using the concepts of stochastic calculus and hedging

4. Apply transformations and similarity solution techniques to PDEs such as Black-Scholes equation and derive analytic solutions.5. Use the analytic formulae to evaluate fair prices for European options

6. Extend the basic European option model (to include dividends, stochastic volatility, stochastic interest rates, early exercise and barriers) and where possible solve the resulting models analytically

Syllabus

1. Introduction to options, futures, no arbitrage principle [3]2. Models for stock prices, basics of stochastic calculus and Ito's lemma. [3]3. Deriving the the pricing partial differential equation, and the assumptions behind it. Formulating the mathematical problem. Analytic solutions and Implied volatility. 34. Connection with the heat conduction equation, solution of the heat conduction equation - similarity solutions and the Dirac delta function. Derivation of the price of European options. [3]5. Extension to consider options on assets paying dividends. [2]6. American options and free boundary problems. [2]7. Interest-rate models and bonds. [2]8. Multi Factor models and Barrier options. [3]

Teaching and learning methods

There are 3 or 4 videos released per week, delivering content from the course .Students are expected to watch the videos, fill in the gaps in the notes, as well as reading and reviewing the notes. Each lecture has a formative assessment attached to test the student's understanding of the lecture. A 1 hour review session highlight some of the more important material from the videos and goes through some of the examples sheets together. A 1 hour feedback tutorial provides an opportunity to work on problems in class, answers and partial solutions will be revealed in class. Finally a coursework test provides an opportunity for students to receive feedback on how well they understand the first half of the course. Students can also get feedback on their understanding directly from the lecturer, either using the Piazza forum or by arranging a meeting during the lecturer's office hour.

Assessment methods

Method Weight
Written exam 80%
Set exercise 20%

Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

Recommended reading

Wilmott, O., Howison, S., Dewynne, J., The Mathematics of Financial Derivatives, Cambridge University Press 1995. ISBN 0521497892

Wilmott, P., 2001: Paul Wilmott Introduces Quantitative Finance, 2nd Edition, Wiley. ISBN: 0471498629. Wilmott, P., 2000: Paul Wilmott on Quantitative Finance, Wiley. ISBN: 0471874388

Study hours

Scheduled activity hours
Lectures 12
Tutorials 12
Independent study hours
Independent study 76

Teaching staff

Staff member Role
Peter Duck Unit coordinator

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