Mathematical Finance

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Welcome to the Department of Economics at the University of Birmingham. Economics teaching and research have a long tradition at Birmingham, dating back to the establishment of the Faculty of Commerce in 1903.

The modern department has about twenty five academic staff members, with a wide range of research interests in areas such as applied economics, economic theory, econometrics, environmental economics, finance and trade.

The department offers a variety of undergraduate programmes, and has an active graduate school involving research students and postgraduates on taught courses.

This programme, taught jointly by the School of Mathematics and the Department of Economics, provides the skills that will enable technically able graduates (including in mathematics, science and engineering) to apply their quantitative training to financial analysis.

In most cases, we expect that graduates from the Masters will take positions in quantitative analysis (or similar) in major financial institutions, such as in the City. The programme should also prepare them for postgraduate research; either to continue in academia or to further qualify for work in financial institutions.

Compulsory Modules
Econometrics with Financial Applications| (15+)
forecasting; stochastic volatility; ARCH; GARCH; co-integration; statistical-arbitrage; non-stationarity; unit roots

Introduction to quantitative finance| (10+)
options pricing; Black-Scholes; European and American options; exotic options; fixed income; binomial method; random walks

Computational Methods and Frontiers| (10+)
finite differences; finite elements; numerical solutions; partial differential equations

Risk Analytics| (10)
copulas; Value-at-Risk; expected shortfall (cVaR); mean-variance portfolio optimization; PCA; stress testing; Black-Litterman; live trading

Optional Modules
International Banking and Finance| (20)

Macroeconomics| (30)
Economic growth, consumption, investment, exchange rates, interest parity conditions, overshooting, speculative attacks, inflation, monetary policy.

Multicriteria Decision Making| (10)
Vector optimization; Pareto efficiency; efficient set; goal programming; partial and total order; invariant order; cone and dual cone.

Nonlinear Programming I| (10)
Optimality condition; convex set and convex function; duality theory; unconstrained optimization; constrained optimization; conjugate gradient algorithms; Newton-type algorithms; interior point algorithms; Lagrangian methods.

Conic optimization |(10)
Interior point algorithms; semi-definite programming; conic optimization; quadratic optimization; Semi-definite relaxation; finance and engineering applications.

Topics in Money and Banking |(10)

Integer Programming| (10)
Alternative formulations; optimality; relaxation; primal and dual bounds; total unimodularity; cut-plane algorithm; branch and bound method; network flow problems; knapsack problems; matching problem; assignment problem; set covering problem

Relevant modules for those without all the requisite undergraduate mathematics training include: PDEs, Transform Theory, and Complex Variable Theory for Physicists. Graduate modules offered elsewhere in the University may also be taken with the Programme Director's approval.

Term 2 (January - March)

Compulsory Modules
Econometrics with Financial Applications| (+15)
forecasting; stochastic volatility; ARCH; GARCH; co-integration; statistical-arbitrage; non-stationarity; unit roots

Exotic options, bonds and further quantitative finance| (+10)
options pricing; Black-Scholes; European and American options; exotic options; fixed income; binomial method; random walks

Computational Methods and Frontiers| (+10)
finite differences; finite elements; numerical solutions; partial differential equations

Economics of Financial Markets |(20)
consumption-based CAPM; equity premium; factor models; time-varying risk; behavioural finance

Optional Modules

Non-Linear Programming II| (10)
Optimality condition; convex set and convex function; duality theory; unconstrained optimization; constrained optimization; conjugate gradient algorithms; Newton-type algorithms; interior point algorithms; Lagrangian methods.

Combinatorial Optimisation |(10)
Alternative formulations; optimality; relaxation; primal and dual bounds; total unimodularity; cut-plane algorithm; branch and bound method; network flow problems; knapsack problems; matching problem; assignment problem; set covering problem

Advanced quantitative finance: crashes, volatility, multiple assets and hedging| (10)
crashes; volatility modeling; multi-asset options; hedging; liquidity; asset allocation; stochastic control; historical lessons; Monte Carlo

Heuristic Optimisation| (10)
Exhaustive search; tapu-search, local search; greedy algorithms; dynamic programming; computer simulation; evolutionary Algorithms.

Research Frontiers in Management Mathematics| (10)
Semi-infinite programming; economic equilibrium problems; projection algorithms; fixed-point methods; merit functions.

Relevant modules for those without all the requisite undergraduate mathematics training include: Numerical Methods in Linear Algebra, Programming. Graduate modules offered elsewhere in the University may also be taken with the Programme Director's approval.

Term 3 (May - June)

Examination Period
July - September
Dissertation (40)

Students are encouraged to pursue internships while writing their dissertations

A good Honours first degree (or overseas equivalent) in Economics or a related discipline. You are expected to have received a good training in economics, to at least intermediate level, and to have a basic knowledge of calculus and statistics.English language requirementsIn order to gain full benefit from your studies, you need to demonstrate that you have a high level of written and spoken English. * IELTS 6.5 with no less than 6.0 in any band * TOEFL 580 Paper-based test /237 Computer-based test English Language Requirements CAE score: (read more) Cambridge English: Advanced (CAE) is part of the Cambridge English suite and is targeted at a high level (IETLS 6.5-8.0). It is an international English language exam set at the right level for academic and professional success. Developed by Cambridge English Language Assessment - part of the University of Cambridge - it helps you stand out from the crowd as a high achiever. 80 (Grade A)

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