MSc Quantitative Finance

Fees for entry in 2027 have not yet been set. For reference, the fees for the academic year beginning September 2026 were as follows:

• MSc (full-time)
  UK students (per annum): £22,600
  International, including EU, students (per annum): £36,800

The fees quoted above are fully inclusive of tuition, administration and computational costs.

Fees for entry are subject to yearly review. The University reserves the right to increase your tuition fee by up to 7% each year for courses lasting more than one year, including to reflect rising costs associated with delivering our educational and wider student experience. Postgraduate fees information .

Always contact the admissions team if you are unsure which fee applies to your qualification award and method of attendance.

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).

We know that student finance can be complicated. The links below provide further information to help guide you.

Learn more about - student finance options for UK students.

Learn more about - fees and finance for international students.

Graduates of The University of Manchester and Manchester Metropolitan University can receive a 10% discount on their master's degree tuition fees as part of our Manchester Alumni Loyalty Discount scheme.

The course will be continually assessed via a series of miniprojects. The project material will cover a range of topics including the solution of nonlinear ODE's, SDEs, lattice (tree) methods, to the solution of the nonlinear partial differential equations, and will require students to write a series of computer programs to solve a specified problem. Students will be assessed on how they analyse the results from their code, by writing coherent reports that explain what they have done, how they did it, and what the results mean.

Please note

Students are not permitted to take, for credit, MATH40082 in an undergraduate programme and then MATH60082 in a postgraduate programme at the University of Manchester, as the courses are identical.

The unit aims to introduce students to scientific computing (specifically computational finance) by means of a variety of numerical techniques, through the use of high-level computing languages. Students will use a combination of writing their own codes, together with the use of templated examples provided as part of the course materials.

To familiarise students with modern numerical approaches and techniques (and capabilities).
 

Students should be able to:  

ILO 1 translate mathematical problems (well defined systems of mathematical equations) into computational tasks.
ILO 2 assess the accuracy of any numerical approximations, through numerical experimentation (and, when possible, by comparison with analytic solution).
ILO 3 process numerical results into a comprehensible form (including the use of standard graphical plotting packages), for presentation in a report.
ILO 4 give a critical assessment of the integrity of numerical methods and results.

1. Introductory C++ course, extra 2hr lab session will be scheduled in the first week [5]
2. Introduction to numerical computation. Numerical approximation and different methodologies. Discussion of errors, roundoff, truncation, discretisation.
3. Monte Carlo simulations; generation of random numbers (including use of antithetic variables). Pricing of European/Vanilla call/put options. Simple path-dependency options (but NO early exercise examples). Assessment of advantages and disadvantages of simulation approach.
4. Binomial tree valuation of European/Vanilla call/put options. Assessment (and improvement) of accuracy. Application to early-exercise put options.
5. Introduction to solution of PDE's using finite-difference methods. Discussion of stability, consistency and convergence. Brief introduction to error analysis. Methods for parabolic equations. CFL condition. Discussion of methods of solution including iterative methods: Jacobi, Gauss-Seidel, SOR, Line relaxation and PSOR methods. Solution of European call/put options using Crank-Nicolson method. Solution of early exercise put options (using PSOR).
6. Advanced techniques: quadrature method, Monte-Carlo Least Squares, body-fitted (free-boundary) coordinate systems.
 

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

- You will normally have approximately 60 minutes of video content. Normally you would spend approximately 2 hrs per week studying the notes and  videos independently
- You will attend a review class discussing the course notes or assignments and demonstrating code - 1hr
- You will attend a lab session demonstrating code and working on problems in class - 2hr
- You will normally have assignments you can be working on - 4hr

Together with the timetabled classes, you should be spending approximately 9 hours per week on this course unit. Extra work may be required during the semester given that there is no end-of-semester assessment.

Lab Classes will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Project reports will be marked up with detailed individual feedback for students.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.
 

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.

G.D. Smith, 'Numerical Solution of Partial Differential Equations', Clarendon Press, Oxford, 1978.
P. Wilmott, S. Howison & J. Dewynne, 'The mathematics of financial derivatives', Cambridge 1995.
J.C. Hull, 'Options, Futures, and Other Derivatives', Sixth Edition, Prentice Hall 2005.
D.J. Higham, 'An introduction to financial option valuation', Cambridge 2004.