Statistics with Financial Mathematics MSc
School of Mathematical and Physical Sciences ,
Faculty of Science
-
Start date
September 2026 -
Duration
1 year 2 years 3 years -
Attendance
Full-time Part-time Distance learning
Explore this course:
Apply now for 2026 entry or register your interest to find out about postgraduate study and events at the University of Sheffield.
Course description
Our MSc Statistics with Financial Mathematics course trains you to apply the probabilistic, statistical and mathematical techniques that are used in the finance industry.
Through our MSc Statistics with Financial Mathematics course you’ll develop the knowledge and experience needed to work in financial services such as banking, insurance and investments. You'll also develop the problem solving and data analysis skills employers value in roles spanning consultancy, data science, public administration and research.
You’ll explore key financial topics such as the Capital Asset Pricing Model, the Black-Scholes option pricing formula, and stochastic processes. In addition to this, you’ll learn important statistical techniques and concepts, including linear and generalised linear modelling and Bayesian statistics. You’ll also master the ability to analyse and draw meaningful conclusions from data, and grow your programming skills using the statistical computing software R.
You’ll spend around a third of your time working on your dissertation, under the supervision of an active researcher who is an expert in their field. This may focus on investigating a data set, or a more theoretical or methodological topic. You’ll blend theoretical knowledge with practical skills, developing project planning, data acquisition, problem specification and analysis skills. You’ll also learn how to present statistical information, and gain experience communicating your findings verbally and in writing.
Examples of recent dissertation topics include:
- Financial modelling with Lévy processes
- Monte Carlo Simulation, Variance Reduction and Applications to Option Pricing
Dissertation topics are often provided by external clients, such as pharmaceutical companies or sports modelling organisations. Distance learning students also often come with projects designed by their employer.
Accreditation
Accredited by the Royal Statistical Society
Modules
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 project.
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 - Bayesian Statistics and Computational Methods
-
This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits - Stochastic Processes and Finance
-
Stochastic processes are models that reflect the wide variety of unpredictable ways in which reality behaves. In this course we study several examples of stochastic processes, and analyse the behaviour they exhibit. We apply this knowledge to mathematical finance, in particular to arbitrage free pricing and the Black-Scholes model.
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
Optional modules:
A student will take 15 credits (one module) from this group.
- 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
Students can also select Languages for All modules.
Year one core modules:
- 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 - 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 project.
15 credits
Year one optional modules:
A student will take 15 credits (one module) from this group.
- 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 - 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 core modules:
- Bayesian Statistics and Computational Methods
-
This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits - Stochastic Processes and Finance
-
Stochastic processes are models that reflect the wide variety of unpredictable ways in which reality behaves. In this course we study several examples of stochastic processes, and analyse the behaviour they exhibit. We apply this knowledge to mathematical finance, in particular to arbitrage free pricing and the Black-Scholes model.
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
Students can also select Languages for All modules not for credit.
Year one core modules:
- 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
Year one optional modules:
A student will take 15 credits (one module) from this group.
- 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
Year two core modules:
- Bayesian Statistics and Computational Methods
-
This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits - 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 project.
15 credits
Students can also select Languages for All modules not for credit.
Year three core modules:
- Stochastic Processes and Finance
-
Stochastic processes are models that reflect the wide variety of unpredictable ways in which reality behaves. In this course we study several examples of stochastic processes, and analyse the behaviour they exhibit. We apply this knowledge to mathematical finance, in particular to arbitrage free pricing and the Black-Scholes model.
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
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 will inform students and take reasonable steps to minimise disruption.
Open days
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Duration
- 1 year full-time
- 2-3 years part-time by distance learning
Teaching
You’ll be taught through lectures, tutorials, computing sessions and group work.
You’ll be expected to spend around 35 hours each week on your studies, with 8 to 12 hours in lectures or computing classes, and the remainder consisting of independent study.
Distance learning option
Our distance learning option is taught online with support via email and an online forum.
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
You'll be assessed in a variety of ways, including project work for some modules, examinations, coursework and a dissertation.
Your career
Employers hire our graduates because of their ability to analyse problems and reach solutions in a clear, precise and logical way. Our courses are designed to give you the skills that will help you succeed in a range of careers, spanning areas such as:
- finance and banking
- consultancy
- data science
- computing and IT
- public administration and policy
Strong mathematical skills open all kinds of doors, whether you want a job that involves doing lots of complex calculations, or one where you help businesses, charities and policymakers to find the best solutions to real-world problems.
Our graduates have been hired by a variety of employers, such as BAE Systems, Barclays, Dell, Deloitte, Goldman Sachs, HSBC, IBM, Lloyds, PwC, Unilever, the Civil Service and the NHS.
You’ll cover advanced topics and gain extensive research training, which is also great preparation if you’d like to pursue a career in research. Sheffield mathematics graduates have secured PhDs at many of the world's top 100 universities.
School
School of Mathematical and Physical Sciences
The School of Mathematical and Physical Sciences is leading the way with groundbreaking research and innovative teaching.
Our mathematicians and statisticians have expertise across pure mathematics, applied mathematics, probability and statistics. We focus on a variety of topics, from the most abstract questions in number theory to the calculations helping to understand climate change.
In the Research Excellence Framework 2021, 96 per cent of our mathematical sciences research was rated in the highest two categories as world-leading or internationally excellent.
Mathematics and statistics students are based in the Hicks Building, which has classrooms, lecture theatres, computer rooms and social spaces.
Entry requirements
Minimum 2:1 undergraduate honours degree in a relevant subject with relevant modules.
We look for applications that demonstrate background within probability, statistics, financial mathematics or actuarial science. Typically we require at least two modules from within these areas, within the final year of undergraduate study.
An introductory course in mathematical analysis (eg real, complex, or stochastic), or other mathematical background equivalent to this level is also required.
Applications with employment history in statistical or financial fields are also welcomed, including for distance learning courses. In such cases we consider the balance of the employment history and academic qualifications.
English language requirements
IELTS 6.5 (with 6 in each component) or University equivalent.
Other requirements
If you have any questions about entry requirements, please contact the school.
Fees and funding
Alumni discount
Save up to £2,500 on your course fees
Are you a Sheffield graduate? You could save up to £2,500 on your postgraduate taught course fees, subject to eligibility.
Apply
You can apply now using our Postgraduate Online Application Form. It's a quick and easy process.
Contact
Any supervisors and research areas listed are indicative and may change before the start of the course.
Recognition of professional qualifications: from 1 January 2021, in order to have any UK professional qualifications recognised for work in an EU country across a number of regulated and other professions you need to apply to the host country for recognition. Read information from the UK government and the EU Regulated Professions Database.