Statistics with Financial Mathematics

Course description

The course trains you to apply the probabilistic, statistical and mathematical techniques that are used in the finance industry.

It's based on our Statistics MSc course, but also includes key financial topics such as the Capital Asset Pricing Model, the Black-Scholes option pricing formula and stochastic processes.

You’ll also develop a detailed working knowledge of more general statistical techniques and concepts, including linear and generalised linear modelling, Bayesian statistics, time series and machine learning.

You’ll learn how to analyse and draw meaningful conclusions from data, and develop your programming skills using the statistical computing software R.

Around one-third of the course is devoted to your dissertation. This may focus on investigating a data set, or a more theoretical or methodological topic. The aim is to give you skills to include on your CV, such as planning and researching a project, data acquisition, problem specification, analysis and reporting your findings.

Dissertation topics are often provided by external clients – for example, pharmaceutical companies or sports modelling organisations. Distance learning students often come with projects designed by their employer.

Weishan Shi shares her experiences of studying the MSc Statistics with Medical Applications course in the School of Mathematics and Statistics.

Accreditation

Accredited by the Royal Statistical Society

Royal Statistical Society (RSS)

Modules

A selection of modules is available each year - some examples are below. There may be changes before you start your course. From May of the year of entry, formal programme regulations will be available in our Programme Regulations Finder.

Core modules:

Financial Mathematics: The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.
10 credits
Machine Learning: Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of “Big Data”, statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits
Time Series: This module considers the analysis of data in which the same quantity is observed repeatedly over time (e.g., recordings of the daily maximum temperature in a particular city, measured over months or years). Analysis of such data typically requires specialised methods, which account for the fact that successive observations are likely to be related. Various statistical models for analysing such data will be presented, as well as how to implement them using the programming language R.
15 credits
Stochastic Processes and Finance: A stochastic process is a mathematical model for phenomena unfolding dynamically and unpredictably over time. This module studies two classes of stochastic process particularly relevant to financial phenomena: martingales and diffusions. The module develops the properties of these processes and then explores their use in Finance. A key problem considered is that of the pricing of a financial derivative such as an option giving the right to buy or sell a stock at a particular price at a future time. What is such an option worth now? Martingales and stochastic integration are shown to give powerful solutions to such questions.
20 credits
The Statistician's Toolkit: This is the first of two 'core' modules students studying on statistics MScs. The aim of this module is to prepare statisticians for the workplace, equipping them with essential statistical modelling, computing and professional skills. The module includes the study of linear and generalised linear modelling, and data analysis using the programming language R.
30 credits
Bayesian Statistics and Computational Methods: This module introduces the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference, and has been the subject of some controversy in the past, but is now widely used. The module also presents various computational methods for implementing both Bayesian and frequentist inference, in situations where obtaining results 'analytically' would be impossible. The methods will be implemented using the programming languages R and Stan, and some programming is taught alongside the theory lectures.
30 credits
Dissertation: The dissertation is an extensive study giving the student the opportunity to synthesise theoretical knowledge with practical skills and giving experience of the phases of a relatively large piece of work: planning to a deadline; researching background information; acquisition and validation of data; problem specification; the carrying through of relevant analyses; and reporting, both at length through the dissertation and in summary, through, for example, a poster display. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.
60 credits

Year one:

Financial Mathematics: The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.
10 credits
Machine Learning: Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of “Big Data”, statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits
The Statistician's Toolkit: This is the first of two 'core' modules students studying on statistics MScs. The aim of this module is to prepare statisticians for the workplace, equipping them with essential statistical modelling, computing and professional skills. The module includes the study of linear and generalised linear modelling, and data analysis using the programming language R.
30 credits
Time Series: This module considers the analysis of data in which the same quantity is observed repeatedly over time (e.g., recordings of the daily maximum temperature in a particular city, measured over months or years). Analysis of such data typically requires specialised methods, which account for the fact that successive observations are likely to be related. Various statistical models for analysing such data will be presented, as well as how to implement them using the programming language R.
15 credits

Year two:

Stochastic Processes and Finance: A stochastic process is a mathematical model for phenomena unfolding dynamically and unpredictably over time. This module studies two classes of stochastic process particularly relevant to financial phenomena: martingales and diffusions. The module develops the properties of these processes and then explores their use in Finance. A key problem considered is that of the pricing of a financial derivative such as an option giving the right to buy or sell a stock at a particular price at a future time. What is such an option worth now? Martingales and stochastic integration are shown to give powerful solutions to such questions.
20 credits
Bayesian Statistics and Computational Methods: This module introduces the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference, and has been the subject of some controversy in the past, but is now widely used. The module also presents various computational methods for implementing both Bayesian and frequentist inference, in situations where obtaining results 'analytically' would be impossible. The methods will be implemented using the programming languages R and Stan, and some programming is taught alongside the theory lectures.
30 credits
Dissertation: The dissertation is an extensive study giving the student the opportunity to synthesise theoretical knowledge with practical skills and giving experience of the phases of a relatively large piece of work: planning to a deadline; researching background information; acquisition and validation of data; problem specification; the carrying through of relevant analyses; and reporting, both at length through the dissertation and in summary, through, for example, a poster display. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.
60 credits

Year one:

The Statistician's Toolkit: This is the first of two 'core' modules students studying on statistics MScs. The aim of this module is to prepare statisticians for the workplace, equipping them with essential statistical modelling, computing and professional skills. The module includes the study of linear and generalised linear modelling, and data analysis using the programming language R.
30 credits
Machine Learning: Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of “Big Data”, statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits

Year two:

Bayesian Statistics and Computational Methods: This module introduces the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference, and has been the subject of some controversy in the past, but is now widely used. The module also presents various computational methods for implementing both Bayesian and frequentist inference, in situations where obtaining results 'analytically' would be impossible. The methods will be implemented using the programming languages R and Stan, and some programming is taught alongside the theory lectures.
30 credits
Time Series: This module considers the analysis of data in which the same quantity is observed repeatedly over time (e.g., recordings of the daily maximum temperature in a particular city, measured over months or years). Analysis of such data typically requires specialised methods, which account for the fact that successive observations are likely to be related. Various statistical models for analysing such data will be presented, as well as how to implement them using the programming language R.
15 credits

Year three:

Financial Mathematics: The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.
10 credits
Stochastic Processes and Finance: A stochastic process is a mathematical model for phenomena unfolding dynamically and unpredictably over time. This module studies two classes of stochastic process particularly relevant to financial phenomena: martingales and diffusions. The module develops the properties of these processes and then explores their use in Finance. A key problem considered is that of the pricing of a financial derivative such as an option giving the right to buy or sell a stock at a particular price at a future time. What is such an option worth now? Martingales and stochastic integration are shown to give powerful solutions to such questions.
20 credits
Dissertation: The dissertation is an extensive study giving the student the opportunity to synthesise theoretical knowledge with practical skills and giving experience of the phases of a relatively large piece of work: planning to a deadline; researching background information; acquisition and validation of data; problem specification; the carrying through of relevant analyses; and reporting, both at length through the dissertation and in summary, through, for example, a poster display. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.
60 credits

The content of our courses is reviewed annually to make sure it's up-to-date and relevant. Individual modules are occasionally updated or withdrawn. This is in response to discoveries through our world-leading research; funding changes; professional accreditation requirements; student or employer feedback; outcomes of reviews; and variations in staff or student numbers. In the event of any change we'll consult and inform students in good time and take reasonable steps to minimise disruption.

Open days

An open day gives you the best opportunity to hear first-hand from our current students and staff about our courses.

You may also be able to pre-book a department visit as part of a campus tour.Open days and campus tours

Duration

1 year full-time
2-3 years part-time by distance learning

Teaching

There are lectures, tutorials, computing sessions and group work. Most statistics lectures are recorded so you can watch them again later.

You’ll be expected to spend around 35 hours each week on your studies, with 8-12 hours in lectures or computing classes, and the remainder consisting of independent study.

Distance learning option

This is taught online with support via email and an online forum. Distance learners also come to the University for residential weeks.

You'll need to be in Sheffield for a few days between late May and early June each year for your exams. You're expected to spend around 20 hours each week on your studies if you're doing the two-year version of the course, and around 12 to 15 hours each week if you're doing the three-year version.

Assessment

Some modules may be continuously assessed through ongoing project work with no examination but most taught modules are assessed by a mixture of examinations and coursework.

The assessment of the dissertation module is based entirely on your submitted dissertation.

Your career

This course is great preparation for roles in the finance sector such as banking, actuarial work, pensions and insurance. Employers that have hired graduates from our School of Mathematics and Statistics in finance roles include Goldman Sachs, Lloyds, Aviva, AXA, Amazon, BAE Systems, Deloitte, PwC and the NHS.

This degree satisfies the eligibility criteria for the Royal Statistical Society’s Graduate Statistician award – a stepping-stone to full professional membership of the RSS and Chartered Statistician status.

I thought a masters degree would help me develop as a mature researcher and that studying abroad would help me to learn a new language

Fatimah Aloef Masters student, Statistics with Financial Mathematics MSc

Following her studies in Saudi Arabia, Fatimah came to Sheffield where she was met by a supportive community within the School of Mathematics.

Department

School of Mathematics and Statistics

A lecturer stood at the front of a seminar by a blackboard

The School of Mathematics and Statistics is one of the biggest departments at the University of Sheffield. It’s home to more than 50 academic staff with expertise across many areas of pure mathematics, applied mathematics, probability and statistics. We aspire to be an inclusive and welcoming environment for all who enjoy mathematics.

Our mathematics and statistics researchers work on a wide variety of topics, from the most abstract questions in algebraic geometry and number theory, to the calculations behind infectious disease, black holes and climate change.

In the Research Excellence Framework 2021, 96 per cent of our research was rated in the highest two categories as world-leading or internationally excellent.

Staff in the School of Mathematics and Statistics have received honours from the Royal Society, the Society for Mathematical Biology and the Royal Statistical Society, who also provide professional accreditation for our statistics courses.

With the support of the London Mathematical Society, we are an organiser of the Transpennine Topology Triangle – a key focal point for topology research in the UK.

We also have strong links with the Society for Industrial and Applied Mathematics, the Institute of Mathematics and its Applications, the European Physical Society and the International Society on General Relativity and Gravitation.

Entry requirements

Minimum 2:1 undergraduate honours degree, with substantial mathematical and statistical components. In particular, you should have studied the following topics and performed well in assessments on them (for example, a score of at least 60 per cent).

Mathematical Methods for Statistics: ideas and techniques from real analysis and linear algebra, including multiple integration, differentiation, matrix algebra, the theory of quadratic forms.
Probability and Probability Distributions: the laws of probability and of conditional probability, the concepts of random variables and random vectors and their distributions, the methodology for calculating with them; laws of large numbers and central limit phenomena.
Basic Statistics: statistical inference, rational decision-making under uncertainty, and how they may be applied in a wide range of practical circumstances; relevant software, for example, R.
Real analysis and stochastic processes: limits of sequences and series, convergence tests, continuity and differentiability, stochastic processes and the Markov property.

Overall IELTS score of 6.5 with a minimum of 6.0 in each component, or equivalent.

Other English language qualifications we accept

If you have any questions about entry requirements, please contact the department.

Fees and funding

The University of Sheffield has scholarships available to support masters students. Students on our MSc Statistics with Financial Mathematics course often have the costs of their degree covered by their employer.

Funding for postgraduate taught courses

Postgraduate study