MSc Financial Mathematics

www.brunel.ac.uk/siscm/mathematical-sciences

SCHOOL OF INFORMATION SYSTEMS, COMPUTING AND MATHEMATICS

MSc in FINANCIAL MATHEMATICS

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.

FACT FILE

MODE OF STUDY

Full time: one year

Part time: two years

ENTRY REQUIREMENTS

You will need a first-class or upper second-class honours degree (or overseas equivalent) 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.

Applicants whose first language is not English will also be required to provide proof of their proficiency in the English language.

ENQUIRIES

The Postgraduate Admissions Secretary Department of Mathematical Sciences

T: +44 (0)1895 265392

E: [email protected]

W: www.brunel.ac.uk/maths

Department of Mathematical Sciences

6361 MSc Financial Mathematics A4 4pg FINAL.indd 1 15/01/2013 12:27

2

MSc in Financial Mathematics Special FeaturesThe Department of Mathematical Sciences, home to its acclaimed research centre CARISMA (www.carisma.brunel.ac.uk), 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 (www.londonmathfinance.org.uk), 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 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. Financial mathematics is a subject that continues to develop. To meet the rapidly evolving industry demand, some of the modules may change over time. A typical set of core and elective modules is as follows.

Core modulesProbability and stochasticsThis module 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 and the Ornstein-Uhlenbeck process.

Financial marketsThis 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 and the Cox-Ross-Rubinstein formula for option pricing.

Option pricing theoryThe 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 and the Black-Scholes formula.

Financial computing I The idea of this module 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 and the Monte Carlo option pricing.

Elective modulesInterest rate theoryAn 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.

Portfolio theoryThe 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 and growth versus income.

Information and financeA modern approach to asset pricing, based on the modelling of the flow of information in financial markets, will be

Department of Mathematical Sciences


www.brunel.ac.uk/siscm/mathematical-sciences 3

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.

Credit risk and structured productsThe 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 regulatory 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 and pricing of credit derivatives.

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 and the Monte Carlo option pricing.

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 projectTowards 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.

AssessmentAssessment 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 to pursue 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, 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.

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.)


Every effort has been made to ensure the accuracy of the information in this brochure and the University will take all reasonable action to deliver these services in accordance with the descriptions set out in it. However, the University reserves the right to vary these services, using all reasonable efforts to offer a suitable alternative. All costs, rates and prices stated in this brochure are subject to amendment and should be taken as a guide only.

4 www.brunel.ac.uk

6361 0113

Career ProspectsGraduates will be equipped to pursue careers in financial institutions and other related industrial sectors in roles such as:

• Financialquant• Riskmanager• Financialinstrumenttrader• Programmer• Riskanalyst• Reinsuranceassessor• Financialreportsofficer

Award-winning Placement and Careers CentreBrunel University’s Placement and Careers Centre (PCC) was named winner for the third year running at the National Placement and Internship Awards in January 2012. The PCC picked up the award for Best University Placement/Careers Service, which celebrates the contributions made by Careers Services in helping students make the most of their work experience opportunities.

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

Part time students pay half the fee in year one, and the other half in year two.

How to apply You can apply online from this page: www.brunel.ac.uk/courses/postgraduate/G330PFINMATH

Professor Dorje Brody – Course LeaderProfessor Brody, Chair in Mathematics and Deputy Head of the Department of Mathematical Sciences, received his MSc and PhD degrees from Imperial College, and subsequently held a research appointment in the Department of Applied Mathematics at Cambridge University, in conjunction with a Research Fellowship at Churchill College. He later returned to Imperial as a Royal Society University Research Fellow. He joined Brunel University in 2011.

Professor Brody’s research interests cover a wide range of topics in applied mathematics. He is the author of “Modern Mathematical Theory of Finance” and “Financial Engineering for Businessmen” both published in Tokyo. He has also authored / co-authored over 100 research papers including various topics on financial mathematics.

He has written an extensive list of industry conference presentations and professional training courses, aimed at finance practitioners on a range of topics including pricing and hedging of equity derivatives, theory of price formation, interest rate theory, weather derivatives pricing, credit risk management, reinsurance pricing, commodities, statistical arbitrage, and stochastic volatility modelling. Together with collaborators he introduced what is now known as the ‘information-based pricing theory’ that aims to significantly improve risk assessment and management.

At Imperial College Professor Brody was heavily involved in the development of the highly successful MSc in Mathematics and Finance. We are delighted that Professor Brody has introduced the MSc in Financial Mathematics to Brunel, starting in September 2013.

…for a practical, imaginative approach…Brunel University is named after the celebrated nineteenth century engineering genius, Isambard Kingdom Brunel, famous for a range of ambitious and highly innovative projects. The ethos of our world-renowned namesake is reflected in the design of our degree courses which combine academic rigour with a practical, entrepreneurial and imaginative approach. And all our courses are underpinned by our research.

…a modern, self-contained campus within a 45-minute tube journey of London…All our up to the minute facilities are located on a single campus which means that everything is close at hand; as are Central London and Heathrow Airport.

…and for excellent student support.Brunel Graduate School organises a range of activities and generic training sessions specifically for postgraduate students.

Students with disabilities are also well looked after at Brunel. For further details, visit www.brunel.ac.uk/life/welfare


Documents

MSc Financial Mathematics