MSc in Statistics with Financial Mathematics
The UK´s statistical tradition, in which empirical and theoretical work continually meet and strengthen each other, has long been recognised as among the best in the world. The Department of Probability & Statistics stands firmly within this tradition, both in its teaching and its research. In recent years a new area of application of probabilistic, statistical and mathematical techniques has emerged in finance, leading to rapid advances in optimal investment, risk management and the pricing of options and derivatives. The new area has seen major development, much of it in the UK, stimulated by the needs of the country´s financial services industry, which is of global as well as national importance. There is a substantial demand for high-quality postgraduate training in this area, including demand for such training in part-time distance-learning form.
The MSc in Statistics with Financial Mathematics provides both a practically-based professional training combining statistics and financial mathematics, and a foundation for those wishing to pursue further research. It is available via distance-learning (2-4 years, part-time) as well as by residential study (1 year full-time). The programme is a development of that leading to the MSc in Statistics, which has been running successfully for many years. It builds on the provision of a firm grounding in practical statistical methodology and computation, including the development of the personal skills in demand by employers, from the established Statistics MSc programme, and adds to them development of an understanding of, and ability to apply, the concepts, models and tools of modern mathematical finance. It provides an excellent foundation for a career in financial areas, or for further study for a research degree.
The established Statistics MSc programme has been supported by national Research Councils for over 35 years. In recent years it has been one of only 6 Statistics MSc courses receiving EPSRC funding.
The programme is kept in close touch with the needs of employers through the programme's Advisory Board, whose members are drawn from industry, commerce and government. Students benefit from contacts with members of the Board, from meetings with employers through open days, from career presentations and through work on dissertation projects arising from commerce and industry.
In the most recent national research assessment exercise (in 2001) the Department´s research received a grade of 5, signifying research of international excellence. Students can be confident that the training offered by the programme is informed by the latest thinking in the subject.
The full-time (residential) and part-time (distant learning) programmes start together with an induction week in Sheffield in September. The full-time course is offered over 12 months, finishing in the following September. The part-time course takes 2, 3 or 4 years to complete. The components other than the dissertation must be completed within three years.
The teaching year is divided into two semesters each of fifteen weeks. Modules giving 120 credits must be taken during this period. The six main modules are each of 20 credits and run through both semesters. Some flexibility is allowed in the programme by the provision of some one-semester 10-credit modules.
All students must take:
- Introductory Mathematical Finance & Time Series (20 credits)
- Stochastic Processes and Finance (20 credits)
- Data Analysis (20 credits)
- Statistical Laboratory (20 credits)
In addition, all students will normally take:
- Linear Modelling (20 credits)
- Inference (20 credits)
except where there is compelling evidence of existing competence based on previous qualifications. In this case two 10-credit modules on Special Topics may replace one of these.
All students complete a Dissertation (60 credits).
Part-time students who take the modules (other than the dissertation) over two years normally take 'Statistical Laboratory', 'Introductory Mathematical Finance & Time Series' and 'Linear Modelling' in year 1 and 'Data Analysis', 'Stochastic Processes and Finance' and 'Inference' in year 2. Those who take the modules (other than the dissertation) over three years take 'Statistical Laboratory' and 'Linear Modelling' in year 1, 'Data Analysis' and 'Introductory Mathematical Finance & Time Series' in year 2 and 'Stochastic Processes and Finance' and 'Inference' in year 3.
Residential students begin work on the dissertation in early Spring, but work on it most intensively during the Summer. The arrangement for part-time students is more flexible but they too are expected to do most of the work during the summers or in the year after they have completed all the other modules.
Successful completion of the programme leads to the award of the MSc with either 'pass' or 'pass with distinction' grade.
The PG Diploma is available for candidates who take only a sub-set of the modules required for the MSc and complete a dissertation, or who take all of the taught part of the MSc but not the dissertation. The PG Certificate is available for candidates who take only a sub-set of the modules and do not undertake the dissertation.
All modules mentioned above are common with the existing MSc in Statistics except for the following core modules:
- Introductory Mathematical Finance & Time Series
In the first half of this course, students are introduced to the key ideas and methods of modern mathematical finance. These include interest rates and bonds, forwards and futures contracts, financial derivatives (European and American options), no-arbitrage pricing, the binomial tree model, risk neutral valuation and the Black-Scholes formula, portfolio optimisation and the capital asset pricing model.
The second half focuses on both computational and mathematical aspects of time series. This includes model building – ARMA, ARIMA and SARIMA, the Box-Jenkins approach to model fitting, forecasting techniques, state space methods and the Kalman filter, and an introduction to spectral techniques.
- Stochastic Processes and Finance
In the first part of this module, we study the probabilistic tools which are essential for modern finance – conditional expectation, martingales, Brownian motion, stochastic integration, Ito´s formula, Girsanov´s theorem, stochastic differential equations and diffusion processes.
In the second half these ideas will be applied to gain a deeper insight into the capital asset pricing model and option pricing. Topics studied will include Markowitz risk and return and Markowitz diversification, the fundamental theorems of asset pricing, change of measure, derivation of the Black-Scholes formula, volatility and the Greeks, pricing and hedging of European options, Monte-Carlo methods for numerical estimation and interest rate modelling