MSc Statistics with Financial Mathematics modules

On this page you can find out about the modules on our MSc Statistics with Financial Mathematics course.

Teaching and learning changes for 2020-21

Due to the coronavirus pandemic we have made some changes to teaching and learning for some courses in the 2020-21 academic year.

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MSc Statistics with Financial Mathematics

Full-time residential (one year)

Financial Mathematics (10 credits)

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 applications in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.

Stochastic Processes and Finance (20 credits)

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.

The Statistician's Toolkit (30 credits)

This is the first of two core modules students studying on statistics MSc's will take. 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.

Bayesian Statistics and Computational Methods (30 credits)

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 programming is taught alongside the theory lectures.

Machine Learning (15 credits)

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.

Time Series (15 credits)

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.

Dissertation (60 credits)

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 at length through the dissertation. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.

Part-time distance learning (two years)

First year

Financial Mathematics (10 credits)

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 applications in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.

The Statistician's Toolkit (30 credits)

This is the first of two core modules students studying on statistics MSc's will take. 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.

Machine Learning (15 credits)

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.

Second year

Stochastic Processes and Finance (20 credits)

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.

Bayesian Statistics and Computational Methods (30 credits)

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 programming is taught alongside the theory lectures.

Time Series (15 credits)

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.

Dissertation (60 credits)

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 at length through the dissertation. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.

Part-time distance learning (three years)

First year

The Statistician's Toolkit (30 credits)

This is the first of two core modules students studying on statistics MSc's will take. 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.

Machine Learning (15 credits)

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.

Second year

Bayesian Statistics and Computational Methods (30 credits)

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 programming is taught alongside the theory lectures.

Time Series (15 credits)

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.

Third year

Financial Mathematics (10 credits)

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 applications in modern finance, and includes a computational project where students further explore some of the ideas of option pricing.

Stochastic Processes and Finance (20 credits)

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.

Dissertation (60 credits)

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 at length through the dissertation. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.

The content of our courses is reviewed annually to make sure it is 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.

Information last updated: 16 September 2020


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