Financial Mathematics MSc

About the Course

Mathematical finance is an area of applied mathematics where concepts and techniques that lie close to the heart of pure mathematics are applied routinely to solve a great variety of important practical problems arising in the day-to-day business of financial institutions. The objective of the MSc in Financial Mathematics is to guide students through to a mastery of the sophisticated mathematical ideas underlying modern finance theory, along with the associated market structures and conventions, with emphasis on: (a) the modelling of financial assets, both in equity markets and in fixed-income markets; (b) the pricing and hedging of options and other derivatives; and (c) the quantification and management of financial risk.

However, mathematical skills alone are not sufficient to implement mathematical ideas in practice. You need numerical and computational methods if you want to put theory into practice and work for a financial institution. We therefore offer a programme that provides a balanced mixture of advanced mathematics (probability theory, stochastic calculus, etc), modern finance theory (derivatives, interest rates, foreign exchange, etc), and computational technique (GPU-based high-performance computing).

The MSc in Financial Mathematics offers a range of exciting modules during the Autumn and the Spring terms, followed by a research project leading to a dissertation to be completed during the Summer term.

Aims

Financial mathematics is a challenging subject, deployed by sophisticated practitioners in financial markets on daily basis. It builds on the application of advanced concepts in modern probability theory to solve various issues faced by industry practitioners in the areas of pricing, hedging, risk management, and beyond. The main objective of the programme is to provide the knowledge needed to be able to enter into this exciting new area of applied mathematics that is widely used in a range of financial markets. 

Main distinguishing features of our programme are:

• We aim to teach some of the key ideas in pricing theory from a modern perspective, using such concepts as pricing kernel and market filtration, as opposed to a more traditional approach based on the historical developments of the subject. 

• We include courses on high-performance computing so that theoretical ideas can be implemented. 

By the end of the year students will gain familiarity with topics including:

• Financial market conventions
• Derivatives market structure
• Theory of stochastics processes
• Option pricing and hedging 
• Interest rate derivatives pricing 
• Portfolio theory
• Price formation 
• Credit risk management
• Numerical implementation
• High-performance computing 

Enquiries

The Postgraduate Admissions Secretary

Department of Mathematical Sciences
Brunel University

Email mscmaths@brunel.ac.uk

Special Features

The Department of Mathematical Sciences, home to its acclaimed research centre CARISMA, has a long tradition of research and software development, in collaboration with various industry partners, in the general area of risk management.

The Department is a member of the London Graduate School in Mathematical Finance, which is a consortium of mathematical finance groups of Birkbeck College, Brunel University, Imperial College London, King’s College London, London School of Economics, and University College London. There is a strong interaction between the financial mathematics groups of these institutions in the greater London area, from which graduates can benefit. In particular there are a number of research seminars that take place regularly throughout the year which students are welcome to attend.

Course Content

Programme structure

The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. There are examinations and coursework in eight modules altogether, including the four core modules. Additionally, all students complete a dissertation.

Core modules

1. Probability and stochastics. This course provides the basics of the probabilistic ideas and mathematical language needed to fully appreciate the modern mathematical theory of finance and its applications. Topics include: measurable spaces, sigma-algebras, filtrations, probability spaces, martingales, continuous-time stochastic processes, Poisson processes, Brownian motion, stochastic integration, Ito calculus, log-normal processes, stochastic differential equations, the Ornstein-Uhlenbeck process.
   
   
2. Financial markets. This course is designed to cover basic ideas about financial markets, including market terminology and conventions. Topics include: theory of interest, present value, future value, fixed-income securities, term structure of interest rates, elements of probability theory, mean-variance portfolio theory, the Markowitz model, capital asset pricing model (CAPM), portfolio performance, risk and utility, portfolio choice theorem, risk-neutral pricing, derivatives pricing theory, Cox-Ross-Rubinstein formula for option pricing.
   
   
3. Option pricing theory. The key ideas leading to the valuation of options and other important derivatives will be introduced. Topics include: risk-free asset, risky assets, single-period binomial model, option pricing on binomial trees, dynamical equations for price processes in continuous time, Radon-Nikodym process, equivalent martingale measures, Girsanov's theorem, change of measure, martingale representation theorem, self-financing strategy, market completeness, hedge portfolios, replication strategy, option pricing, Black-Scholes formula.
   
   
4. Financial computing I. The idea of this course is to enable students to learn how the theory of pricing and hedging can be implemented numerically. Topics include: (i) The Unix/Linux environment, C/C++ programming: types, decisions, loops, functions, arrays, pointers, strings, files, dynamic memory, preprocessor; (ii) data structures: lists and trees; (iii) introduction to parallel (multi-core, shared memory) computing: open MP constructs; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.

Elective modules

1. Interest rate theory. An in-depth analysis of interest-rate modelling and derivative pricing will be presented. Topics include: interest rate markets, discount bonds, the short rate, forward rates, swap rates, yields, the Vasicek model, the Hull-White model, the Heath-Jarrow-Merton formalism, the market model, bond option pricing in the Vasicek model, the positive interest framework, option and swaption pricing in the Flesaker-Hughston model.
   
   
2. Portfolio theory. The general theory of financial portfolio based on utility theory will be introduced in this module. Topics include: utility functions, risk aversion, the St Petersburg paradox, convex dual functions, dynamic asset pricing, expectation, forecast and valuation, portfolio optimisation under budget constraints, wealth consumption, growth versus income.
   
   
3. Information and finance. A modern approach to asset pricing, based on the modelling of the flow of information in financial markets, will be introduced in this module. Topics include: information-based asset pricing - a new paradigm for financial risk management; modelling frameworks for cash flows and market information; applications to credit risk modelling, defaultable discount bond dynamics, the pricing and hedging of credit-risky derivatives, asset dependencies, and the origin of stochastic volatility; gamma information and the pricing of reinsurance contracts; valuation of aggregate claims; complex cash-flow structures.
   
   
4. Credit risk and structured products. The worldwide financial crisis of recent years has drawn attention to the pressing need for robust modern methods in the field of credit risk management, which remains an area of key concern to financial institutions and regulator authorities. This course provides an introduction to the main ideas and techniques of credit risk analysis. Topics include: markets for credit-related products, issues to do with correlations and credit migration, credit default swaps (CDS), collateralized debt obligations (CDO), jump processes, credit risky bonds, market sentiment and randomly-timed default, hazard rates and forward hazard rates, options on defaultable bonds, pricing models for credit-risky bonds, pricing of credit derivatives.
   
   
5. Financial computing II: High performance computing. In this parallel-computing module students will learn how to harness the power of a multi-core computer and Open MP to speed up a task by running it in parallel. Topics include: shared and distributed memory concepts; Message Passing and introduction to MPI constructs; communications models, applications and pitfalls; open MP within MPI; introduction to Graphics Processors; GPU computing and the CUDA programming model; CUDA within MPI; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.
   
   
6. Statistics. The idea of this module is to enable students to learn a variety of statistical techniques that will be useful in various practical applications in investment banks and hedge funds. Topics include: probability and statistical models, models for return distributions, financial time series, stationary processes, estimation of AR processes, portfolio regression, least square estimation, value-at-risk, coherent risk measures, GARCH models, non-parametric regression and splines.

Research project

Towards the end of the Spring Term, students will choose a topic to work on, which will lead to the preparation of an MSc dissertation. This can be thought of as a mini research project. The project supervisor will usually be a member of the financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

Assessment

Assessment is by a combination of coursework, examination, and dissertation. Examinations are held in May. The MSc degree is awarded if the student reaches the necessary overall standard on the taught part of the course and submits a dissertation that is judged to be of the required standard. Specifically, to qualify for the MSc degree, the student must: (a) take examinations in eight modules including the four core modules, (b) pass at least seven modules, and (c) submit a dissertation of the required standard. If a student does not achieve the requirements for the degree of MSc, they may, if eligible, be awarded a Postgraduate Diploma.

Employability

The modelling and management of financial risk is an expanding field worldwide, offering numerous opportunities for fulfilling and engaging careers. Our graduates will be well positioned for pursuing jobs in a number of different areas of financial modeling and risk management in the financial services industry, with employment prospects in banks, asset management firms, hedge funds, insurance companies, exchanges, corporate and sovereign treasuries, financial software developers, financial regulators, and financial publishing houses. There is also a demand in financial institutions for well qualified mathematically literate graduates with higher degrees for positions in the trading, structuring and marketing of financial products.

Fees for 2013/14 entry

The fees for the 2013-2014 academic year are £17,500 on a full-time basis, both for home/EU and for overseas students.

Read about funding opportunities available to postgraduate students

Fees quoted are per annum and are subject to an annual increase.

Entry Requirements

For consideration for admission to the MSc in Financial Mathematics we require (the equivalent of) a first-class or upper second-class honours degree in mathematics, or in a subject with a substantial mathematics content (such as physics or engineering) where the student has taken several modules of mathematics courses and has proven mathematical ability.

Heading: Mature students and part-time students

In addition to applications from recent graduates, we welcome applications from mature candidates who (for example) might already be working in the financial services and wish to take a break from employment for a year to pursue the MSc in Financial Mathematics at Brunel to advance their careers.

We also offer students the opportunity to pursue the MSc in Financial Mathematics on a part-time basis over a two-year period. (No evening courses are available.)

English Language Requirements

Brunel also offers our own BrunELT English Test and accept a range of other language courses. We also have a range of Pre-sessional English language courses, for students who do not meet these requirements, or who wish to improve their English.