Financial Mathematics MSc

Overview

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 the world's financial institutions.

The objective of the Brunel 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:

• the modelling of the dynamics of financial assets, both in equity markets and in fixed-income markets
• the pricing and hedging of options and other derivatives
• the quantification and management of financial risk.

Candidates are also provided with the means to master the numerical and computational skills necessary for the practical implementation of financial models, thus enabling you to put theory into practice and putting you in a good position to carry out work for a financial institution. We therefore offer a programme that provides a balanced mixture of advanced mathematics (including modern probability theory and stochastic calculus), modern finance theory (including models for derivatives, interest rates, foreign exchange, equities, commodities, and credit), 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 an individual research project leading to a dissertation that is completed during the Summer term.

Aims

Financial mathematics is a challenging subject, the methods of which are deployed by sophisticated practitioners in financial markets on a daily basis. It builds on the application of advanced concepts in modern probability theory to enable market professionals to tackle and systematically resolve a huge range of issues in the areas of pricing, hedging, risk management, and market regulation. The main objective of the Brunel MSc in Financial Mathematics is to provide candidates with the knowledge they need to be able to enter into this exciting new area of applied mathematics and to position themselves for the opportunity to work in financial markets.

Among the main distinguishing features of our programme are the following:

• We aim to teach the key ideas in financial asset pricing theory from a thoroughly modern perspective, using concepts and methods such as pricing kernels, market information filtrations, and martingale techniques, as opposed say to the more traditional but old-fashioned approach based on the historical development of the subject.
• In our programme candidates are asked at each stage to undertake a critical re-examination of the hypotheses implicit in any financial model, with a view to gaining a clear grasp of both its strengths and its limitations.
• The programme includes courses on high-performance computing that provide candidates with the techniques whereby financial models can be implemented.

By the end of the year students will gain familiarity with a range of highly relevant topics, including:

• Financial market conventions
• Derivative market structures
• Stochastic calculus
• Option pricing and hedging
• Interest rate theory
• Dynamic portfolio theory
• Market information and price formation
• Credit risk management
• Numerical implementation of financial models
• High-performance computing.

Course content

Programme structure

The programme offers six "compulsory" modules, taken by all, along with three elective modules from which you choose two modules. There are lectures, examinations and coursework in eight modules altogether, including the six compulsory modules. Additionally, all students complete an individual research project on a selected topic in financial mathematics, leading to the submission of a dissertation.

Compulsory modules

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.

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.

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.

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.

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.

Research methods and case studies. The aims of this module are to develop students' knowledge and critical awareness of a variety of research methods; encourage students to develop critical thinking and transferable skills appropriate to their discipline; enable students to develop an understanding of the current needs of industry and commerce; and prepare students for their dissertation.

Financial Mathematics Dissertation

Towards the end of the Spring Term, students will choose a topic for an individual research project, which will lead to the preparation and submission of an MSc dissertation. The project supervisor will usually be a member of the Brunel financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

Elective modules

Information in finance with application to credit risk management. An innovative and intuitive 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 such as credit default swaps (CDS), asset dependencies and correlation modelling, and the origin of stochastic volatility.

Financial computing II. 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.

Statistics for finance. This module covers: (a) return and loss distributions: statistical properties of return distributions, tests for normality and QQ plots, heavy-tail distributions; (b) risk measures: value-at-risk, expected shortfall, estimation of risk measures, coherent risk measures, forecasting risk measures,  backtesting methods; and (c) time series models: mean, autocovariance, autocorrelation, stationarity, parameter estimation, model selection and forecasting, white noise process, autoregressive and moving average (ARMA) processes, generalized autoregressive conditional heteroscedasticity (GARCH) processes, forecasting risk measures using these processes.

Read more about the structure of postgraduate degrees at Brunel and what you will learn on the course.

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 modelling and risk management in the financial services industry, with employment prospects in banks, asset management firms, hedge funds, pension funds, insurance and re-insurance companies, exchanges, corporate and sovereign treasuries, financial consultants, financial software developers, financial regulators, financial publishing houses, and companies specialising in the analysis and distribution of financial information and data. 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.

Entry criteria 2019/20

• A 2:2 (or above) UK Honours degree, or equivalent internationally recognised qualification, in Mathematics.
• Applications from candidates with degrees in related subjects with a substantial mathematical component (such as Physics, Engineering, Chemistry, or Economics) may be considered on an individual basis.
• Other qualifications with relevant work experience may also be considered.

Entry criteria are subject to review and change each academic year.

International and EU entry requirements

Assessment and feedback

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 compulsory modules, (b) attain the minimum grade profile (or better) required for a Masters degree 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.

The modules will be taught by:

Dr Elena Boguslavskaya
Dr Paresh Date (Course Director)
Dr Anne-Sophie Kaloghiros
Dr Matthias Maischak
Dr David Meier
Dr Veronica Vinciotti

Special features

The Department of Mathematics, 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 London, 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.

Fees and funding

Fees for 2019/20 entry

UK/EU students: £10,140 full-time; £5,070 part-time

International students: £18,720 full-time; £9,360 part-time

Some courses incur additional course related costs. You can also check our on-campus accommodation costs for more information on living expenses.

Read about funding opportunities available to postgraduate students

UK/EU students can opt to pay in six equal monthly instalments: the first instalment is payable on enrolment and the remaining five by Direct Debit or credit/debit card.

Overseas students can opt to pay in two instalments: 60% on enrolment, and 40% in January for students who commence their course in September (or the remaining 40% in March for selected courses that start in January).

Fees quoted are per year and may be subject to an annual increase. Home/EU undergraduate student fees are regulated and are currently capped at £9,250 per year; any changes will be subject to changes in government policy. International and postgraduate fees will increase annually in line with RPI, or 5%, whichever is the lesser.

There is a range of financial support available to help you fund your studies. Find out about postgraduate student funding options.