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Masters Degrees (Stochastic Calculus)

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The programme provides graduates with strong mathematical skills, the necessary computational techniques and finance background relevant to subsequent employment in a sector of finance such as investment banks, hedge funds, insurance companies and the finance departments of large corporations where mathematics plays a key role. Read more
The programme provides graduates with strong mathematical skills, the necessary computational techniques and finance background relevant to subsequent employment in a sector of finance such as investment banks, hedge funds, insurance companies and the finance departments of large corporations where mathematics plays a key role.

The depth of the mathematics taught should enable graduates to pursue research careers in stochastic analysis, financial mathematics or other relevant areas.

The period October to June is devoted to lectures, tutorials and practical sessions comprising the core and optional modules. This is followed by a period of about 14 weeks devoted to an individual project.

Core study areas include measure theory and martingales, stochastic models in finance, stochastic calculus and theory of stochastic pricing and a research project.

Optional study areas include programming and numerical methods, regular and chaotic dynamics, financial economics, functional analysis, elements of PDEs, static and dynamic optimisation, asset management and derivatives, and corporate finance

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/mathematics/mathematical-finance/

Programme modules

Semester 1:
Compulsory Modules
- Introduction to Measure Theory and Martingales
- Stochastic Models in Finance

Optional Modules (choose two)
- Programming and Numerical Methods
- Regular and Chaotic Dynamics
- Financial Economics

Semester 2:
Compulsory Modules
- Stochastic Calculus and Theory of Stochastic Pricing
- Research Project

Optional Modules (choose three)
- Functional Analysis
- Elements of PDEs
- Static and Dynamic Optimisation
- Either Asset Management and Derivatives or Corporate Finance

Assessment

A combination of written examinations, reports, individual and group projects, and verbal presentations.

Careers and further study

This programme may lead to a wide range of employment within industry, the financial sectors, and research establishments. It may also provide an ideal background for postgraduate research in Stochastic Analysis, Probability Theory, Mathematical Finance and other relevant areas.

Scholarships and sponsorships

A number of part-fee studentships may be available to appropriately qualified international students.

Why choose mathematics at Loughborough?

Mathematics at Loughborough has a long history of innovation in teaching, and we have a firm research base with strengths in both pure and applied mathematics as well as mathematics education.

The Department comprises more than 34 academic staff, whose work is complemented and underpinned by senior visiting academics, research associates and a large support team.

The programmes on offer reflect our acknowledged strengths in pure and applied research in mathematics, and in some cases represent established collaborative training ventures with industrial partners.

- Mathematics Education Centre (MEC)
The Mathematics Education Centre (MEC) at Loughborough University is an internationally renowned centre of research, teaching, learning and support. It is a key player in many high-profile national initiatives.
With a growing number of academic staff and research students, the MEC provides a vibrant, supportive community with a wealth of experience upon which to draw.
We encourage inquiries from students who are interested in engaging in research into aspects of learning and teaching mathematics at Masters, PhD and Post Doc levels. Career prospects With 100% of our graduates in employment and/or further study six months after graduating, career prospects are excellent. Graduates go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

- Career prospects
With 100% of our graduates in employment and/or further study six months after graduating, career prospects are excellent. Graduates
go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/mathematics/mathematical-finance/

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This masters is run jointly with Heriot-Watt University. It provides you with expertise in financial mathematics, including stochastic calculus, and a range of practical techniques for analysing financial markets. Read more

Programme description

This masters is run jointly with Heriot-Watt University. It provides you with expertise in financial mathematics, including stochastic calculus, and a range of practical techniques for analysing financial markets. You will also learn quantitative skills for developing and managing risk that are in high demand since the recent financial crisis.

Adding depth to your learning, our work placement programme puts you at the heart of organisations such as Aberdeen Asset Management, Barrie & Hibbert and Lloyds Banking Group.

Programme structure

This programme involves two taught semesters of compulsory and option courses, followed by a dissertation project.

Compulsory courses:

Credit Risk Modelling
Derivatives Markets
Derivative Pricing and Financial Modelling
Discrete-Time Finance
Financial Markets
Special Topics 1
Special Topics 2
Stochastic Analysis in Finance

Option courses:

Deterministic Optimization Methods in Finance
Financial Econometrics
Portfolio Theory
Numerical Techniques of Partial Differential Equations
Optimization Methods in Finance
Simulation
Statistical Methods
Statistical Inference
Time Series Analysis
Stochastic Control and Dynamic Asset Allocation

Career opportunities

Graduates typically work in major financial institutions or continue their studies by joining PhD programmes.

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This masters programme covers the advanced mathematics that has revolutionised finance since the works of Black, Scholes and Merton in the early seventies. Read more
This masters programme covers the advanced mathematics that has revolutionised finance since the works of Black, Scholes and Merton in the early seventies. This programme is aimed at those students who are passionate about mathematics and driven to make a career amongst the many and varied financial institutions throughout the world.

The programme, which is part of the Maxwell Institute for Mathematical Sciences, the joint research institute of mathematical sciences at the University of Edinburgh and Heriot-Watt University, provides an intensive training in the mathematical ideas and tools vital to the finance industry. By developing essential new mathematical concepts, especially in stochastic calculus, and placing the mathematics in the contexts of financial markets, derivative pricing and credit risk, the programme equips students for a range of exciting and potentially lucrative career opportunities.

The programme is delivered jointly between Heriot-Watt University and the University of Edinburgh. This means you will be enrolled as a student at both univerities and benefit from access to all the services and facilities each university has to offer.

Teaching is delivered by renowned academics from both Heriot-Watt and the University of Edinburgh - some classes will therefore take place at Heriot-Watt's campus and others at the University of Edinburgh campus. Successful students will graduate with a degree awarded jointly by Heriot-Watt and the University of Edinburgh and both names will appear on the graduation certificate.

Programme content

Core courses

Derivatives Markets
Derivative Pricing and Financial Modelling
Financial Markets
Discrete-Time Finance
Stochastic Analysis in finance
Credit Risk Modelling
Special Topics, including industry lead projects

Options

Statistical Methods
Financial Econometrics
Time Series Analysis
Modern Portfolio Theory
Optimisation Methods in Finance
Numerical Methods for PDEs
Simulation in Finance
Deterministic Optimisation Methods in Finance

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MSc Risk Management & Financial Engineering is a highly quantitative programme tailored to high calibre and technically-minded graduates wanting a deeper, more analytical study of risk management and financial engineering than is found in general finance programmes. Read more
MSc Risk Management & Financial Engineering is a highly quantitative programme tailored to high calibre and technically-minded graduates wanting a deeper, more analytical study of risk management and financial engineering than is found in general finance programmes.

The programme is accredited by the Professional Risk Managers’ International Association (PRMIA) and the School offers students on this programme the opportunity to attend PRMIA events, have access to its resources and receive considerable discounts on PRMIA exams.

The programme

In September you will study five foundation modules to introduce the tools of modern finance and enhance your career development skills. These include:
• Markets and Securities
• Financial Modelling
• Application of Matlab to Finance
• Data Structures and Algorithms using Python
• The Finance Industry

You’ll take eight core modules which are the backbone of our programme, providing you with a solid knowledge base in each subject area. Each module builds on previous experience while introducing new and challenging disciplines. These include:
• Empirical Finance: Methods and Applications
• Financial Engineering
• Financial Statistics
• Investments and Portfolio Management
• Risk Management and Valuation
• Stochastic Calculus

You will also receive training in Visual Basic for Applications (VBA), choose from a variety of electives and undertake a final project. The selection of electives include:
• Advanced Options Theory
• Credit Risk
• Advanced Financial Statistics
• Enterprise Risk Management
• Fixed Income Securities
• International Elective: Macro and Finance for Practitioners
• International Finance
• Insurance
• Structured Credit and Equity Products
• Private Equity and Venture Capital
• Wealth Management and Alternative Investments
• Topics in FinTech Innovation
• Big Data in Finance

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This highly focused MSc explores some of the mathematics behind modern secure information and communications systems, specialising in mathematics relevant for public key cryptography, coding theory and information theory. Read more
This highly focused MSc explores some of the mathematics behind modern secure information and communications systems, specialising in mathematics relevant for public key cryptography, coding theory and information theory. During the course critical awareness of problems in information transmission, data compression and cryptography is raised, and the mathematical techniques which are commonly used to solve these problems are explored.

The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography and our academic staff include several leading researchers in these areas. Students on the programme have the opportunity to carry out their dissertation projects in cutting-edge research areas and to be supervised by experts.

The transferable skills gained during the MSc will open up a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsofcryptographyandcommunications(msc).aspx

Why choose this course?

- You will be provided with a solid mathematical foundation and a knowledge and understanding of the subjects of cryptography and communications preparing you for research or professional employment in this area.

- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.

- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.

- After completing the course former students have a good foundation for the next step of their career both inside and outside academia.

Department research and industry highlights

The members of the Mathematics Department cover a range of research areas. There are particularly strong groups in information security, number theory, quantum theory, group theory and combinatorics. The Information Security Group has particularly strong links to industry.

Course content and structure

You will study eight courses as well as complete a main project under the supervision of a member of staff.

Core courses:
Advanced Cipher Systems
Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed as well as methods for obtaining confidentiality and authentication.

Channels
In this unit, you will investigate the problems of data compression and information transmission in both noiseless and noisy environments.

Theory of Error-Correcting Codes
The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Public Key Cryptography
This course introduces some of the mathematical ideas essential for an understanding of public key cryptography, such as discrete logarithms, lattices and elliptic curves. Several important public key cryptosystems are studied, such as RSA, Rabin, ElGamal Encryption, Schnorr signatures; and modern notions of security and attack models for public key cryptosystems are discussed.

Main project
The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Additional courses:
Applications of Field Theory
You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory
‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms
In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics
In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

Combinatorics
The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory
You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory
Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.

On completion of the course graduates will have:
- a suitable mathematical foundation for undertaking research or professional employment in cryptography and/or communications

- the appropriate background in information theory and coding theory enabling them to understand and be able to apply the theory of communication through noisy channels

- the appropriate background in algebra and number theory to develop an understanding of modern public key cryptosystems

- a critical awareness of problems in information transmission and data compression, and the mathematical techniques which are commonly used to solve these problems

- a critical awareness of problems in cryptography and the mathematical techniques which are commonly used to provide solutions to these problems

- a range of transferable skills including familiarity with a computer algebra package, experience with independent research and managing the writing of a dissertation.

Assessment

Assessment is carried out by a variety of methods including coursework, examinations and a dissertation. The examinations in May/June count for 75% of the final average and the dissertation, which has to be submitted in September, counts for the remaining 25%.

Employability & career opportunities

Our students have gone on to successful careers in a variety of industries, such as information security, IT consultancy, banking and finance, higher education and telecommunication. In recent years our graduates have entered into roles including Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security manager at London Underground.

How to apply

Applications for entry to all our full-time postgraduate degrees can be made online https://www.royalholloway.ac.uk/studyhere/postgraduate/applying/howtoapply.aspx .

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This course covers a wide range of topics from both applied and applicable mathematics and is aimed at students who want to study the field in greater depth, in areas which are relevant to real life applications. Read more
This course covers a wide range of topics from both applied and applicable mathematics and is aimed at students who want to study the field in greater depth, in areas which are relevant to real life applications.

You will explore the mathematical techniques that are commonly used to solve problems in the real world, in particular in communication theory and in physics. As part of the course you will carry out an independent research investigation under the supervision of a member of staff. Popular dissertation topics chosen by students include projects in the areas of communication theory, mathematical physics, and financial mathematics.

The transferable skills gained on this course will open you up to a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsforapplications.aspx

Why choose this course?

- You will be provided with a solid mathematical foundation and knowledge and understanding of the subjects of cryptography and communications, preparing you for research or professional employment in this area.

- The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography. The academics who teach on this course include several leading researchers in these areas.

- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.

- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.

- After completing the course students have a good foundation for the next step of their career both inside and outside academia.

Department research and industry highlights

The members of the Mathematics Department cover a range of research areas. There are particularly strong groups in information security, number theory, quantum theory, group theory and combinatorics. The Information Security Group has particularly strong links to industry.

Course content and structure

You will study eight courses and complete a main project under the supervision of a member of staff.

Core courses:
Theory of Error-Correcting Codes
The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Advanced Cipher Systems
Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed, as well as methods for obtaining confidentiality and authentication.

Main project
The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Additional courses:
Applications of Field Theory
You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory
‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms
In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics
In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

Combinatorics
The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory
You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory
Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.

On completion of the course graduates will have:
- knowledge and understanding of: the principles of communication through noisy channels using coding theory; the principles of cryptography as a tool for securing data; and the role and limitations of mathematics in the solution of problems arising in the real world

- a high level of ability in subject-specific skills, such as algebra and number theory

- developed the capacity to synthesise information from a number of sources with critical awareness

- critically analysed the strengths and weaknesses of solutions to problems in applications of mathematics

- the ability to clearly formulate problems and express technical content and conclusions in written form

- personal skills of time management, self-motivation, flexibility and adaptability.

Assessment

Assessment is carried out by a variety of methods including coursework, examinations and a dissertation. The examinations in May/June count for 75% of the final average and the dissertation, which has to be submitted in September, counts for the remaining 25%.

Employability & career opportunities

Our students have gone on to successful careers in a variety of industries, such as information security, IT consultancy, banking and finance, higher education and telecommunication. In recent years our graduates have entered into roles including Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security Manager at London Underground.

How to apply

Applications for entry to all our full-time postgraduate degrees can be made online https://www.royalholloway.ac.uk/studyhere/postgraduate/applying/howtoapply.aspx .

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Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes. Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Read more
Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes: Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Postgraduate loans are also available to English and Welsh domiciled students. For more information on fees and funding please visit our website.

The MRes in Stochastic Processes: Theory and Application is delivered through optional modules for the taught element followed by a large research project that contributes to the field in an explicit way, rather than merely applying existing knowledge.

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

The Department’s research groups include:

Algebra and Topology Group
Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group
Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group
Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multi-fractal and multi-scale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group
Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing.

Key Features

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

Course Content

As a student on the MRes Stochastic Processes programme you will study a range of topics for the taught element including:

Stochastic Calculus based on Brownian Motion
Levy processes and more general jump processes
The advanced Black-Scholes theory
Theory and numerics of parabolic differential equations
Java programming

The Stochastic Processes: Theory and Application course consists of a taught part (60 credits) and a research project (120 credits). Students will have a personal supervisor for their research project from the start of their studies.

Research projects could be of a theoretical mathematical nature, or they could be more applied, for example in financial mathematics or actuarial studies. Some of the research projects will be of an interdisciplinary character in collaboration with some of Swansea's world class engineers. For such projects it is likely that EPSRC funding would be available.

Facilities

The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use. It is a popular venue for students to work independently on the regular example sheets set by their lecturers, and to discuss Mathematics together.

Our main university library, Information Services and Systems (ISS), contains a notably extensive collection of Mathematics books.

Careers

The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistical analysis, marketing and sales.

Some of our students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where maths graduates will find plenty of career opportunities.

Research

The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

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This programme provides an exciting opportunity to gain an insight into the pressing economic issues of our times and learn how to assess, adapt and apply modern macroeconomic and microeconomic models to shape organisational or government policy. Read more
This programme provides an exciting opportunity to gain an insight into the pressing economic issues of our times and learn how to assess, adapt and apply modern macroeconomic and microeconomic models to shape organisational or government policy.

Our programme is designed to equip you with the skills of a professional economist, for careers in government, international organisations and business.

You will learn to understand and model issues affecting financial markets through the lens of an economist, assessing both the microeconomic impacts for firms, as well as the macroeconomic implications for the global economy.

You will develop advanced theoretical and quantitative skills, highly sought after by employers in the financial services sectors of industry and government, as well as transferable skills that will be of value for a range of other sectors.

There is the opportunity to specialise in various fields of finance. All students register for the MSc in Economics and Finance. However, depending on the choice and availability of modules and dissertation topic, it is possible to graduate with an MSc in Financial Economics instead.

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/business-economics/economics-finance/

Programme modules

Semester 1:
Compulsory Modules
- Macroeconomics Analysis
- Microeconomics Analysis
- Research Communication (two-semester module)
- Research Methods

Optional Modules (choose one)
- Financial Economics
- Introduction to Measure Theory and Martingales
- Stochastic Models in Finance
- The Financial System

Semester 2:
Compulsory Modules
- Further Quantitative Techniques for Finance and Economics
- Research Communication (two semester module)

Optional Modules (choose three)
- Applied Banking and Financial Modelling
- Asset Management and Derivatives
- Banking and Financial Markets
- Comparative Banking
- Corporate Finance
- Credit Risk Management
- Development Finance
- Economics and Energy Policy
- Stochastic Calculus and Theory of Stochastic Pricing

Choice of Semester 2 modules may be restricted by the option selected in Semester 1. The School reserves the right to vary the list of optional modules.

Summer:
- Dissertation

Assessment

75% examination and 25% coursework for most modules.

Careers and further study

Well-trained, numerate economists are in high demand in every sector. This programme prepares you for a career as a professional economist in banking, education, finance, government or industry, and for higher awards by research.

Example destinations include:
- HSBC – Analyst;
- SSR Group (Sweden) – Associate FX Broker;
- Siemens – Finance Officer.

Scholarships and sponsorships

School awards may be available for high-calibre national and international students.

Why choose business and economics at Loughborough?

Loughborough’s School of Business and Economics is a thriving forward-looking centre of education that aims to provide an exceptional learning experience.

Consistently ranked as a Top-10 UK business school by national league tables, our graduates are highly employable and enjoy starting salaries well above the national average.

The rich variety of postgraduate programmes we offer ranges from taught masters, MBA and doctoral programmes, to short courses and executive education, with subjects spanning Management, Marketing, Finance and Economics, Work Psychology, Business Analytics, International Crisis Management and Information Management. New for 2016, we are also launching two exciting new programmes in Human Resource Management. All of this contributes to a lively and supportive learning environment within the School.

- Internationally Accredited
The School of Business and Economics is one of less than 1% of business schools in the world to have achieved accreditation from all three major international accrediting bodies: The Association to Advance Collegiate Schools of Business (AACSB International), EQUIS accreditation from the European Foundation for Management Development (EFMD) and the Association of MBAs (AMBA).

- Career Prospects
Our graduates are in great demand. Over 94% of our postgraduate students were in work and/or further study six months after graduating.* As such, you will be equipped with skills and knowledge that will serve you well in your career or enable you to pursue further study and research.

*Source: DLHE

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/business-economics/economics-finance/

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This programme is ideal for those who wish to pursue a career in the financial services sectors of industry or government, particularly banking and central banking. Read more
This programme is ideal for those who wish to pursue a career in the financial services sectors of industry or government, particularly banking and central banking.

Our modules are underpinned by the latest research and best practice, having been designed to equip you with up-to-date and relevant knowledge across a number of areas, including banking, finance and research methods.

The range of optional modules on the programme will enable you to specialise in areas of economics, banking and finance that best suit your career ambitions and interests.

Core study areas include financial economics, the financial system, research communication, research methods, asset management and derivatives, corporate finance, banking and financial markets, and further quantitative techniques.

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/business-economics/banking-finance/

Programme modules

Semester 1:
Compulsory modules
- Financial Economics
- Research Methods
- The Financial System
- Research Communication (two-semester module)

Optional modules (choose one):
- Introduction to Measure Theory and Martingales
- Macroeconomic Analysis
- Microeconomic Analysis
- Stochastic Models in Finance

Semester 2:
Core modules
- Asset Management and Derivatives and/or Corporate Finance
- Banking and Financial Markets
- Further Quantitative Techniques for Finance and Economics
- Research Communication (two-semester module)

Optional modules (choose one):
- Applied Banking and Financial Modelling
- Comparative Banking
- Development Finance
- Stochastic Calculus and Theory of Stochastic Pricing

Summer period:
Students satisfy the research requirement by examined participation in research seminars. Subject to special conditions, students may submit a dissertation instead.

Assessment

Modules are assessed by a combination of examinations and assignments.

Careers and further study

Example destinations include:
- Bank of China – Senior Manager
- China Everbright Bank – Client Manager
- Deutsche Bank – Analyst
- KPMG – Audit Associate
- National Australia Bank – Senior Assistant in Research
- RBS – Financial Transfer Officer

Why choose business and economics at Loughborough?

Loughborough’s School of Business and Economics is a thriving forward-looking centre of education that aims to provide an exceptional learning experience.

Consistently ranked as a Top-10 UK business school by national league tables, our graduates are highly employable and enjoy starting salaries well above the national average.

The rich variety of postgraduate programmes we offer ranges from taught masters, MBA and doctoral programmes, to short courses and executive education, with subjects spanning Management, Marketing, Finance and Economics, Work Psychology, Business Analytics, International Crisis Management and Information Management. New for 2016, we are also launching two exciting new programmes in Human Resource Management. All of this contributes to a lively and supportive learning environment within the School.

- Internationally Accredited
The School of Business and Economics is one of less than 1% of business schools in the world to have achieved accreditation from all three major international accrediting bodies: The Association to Advance Collegiate Schools of Business (AACSB International), EQUIS accreditation from the European Foundation for Management Development (EFMD) and the Association of MBAs (AMBA).

- Career Prospects
Our graduates are in great demand. Over 94% of our postgraduate students were in work and/or further study six months after graduating.* As such, you will be equipped with skills and knowledge that will serve you well in your career or enable you to pursue further study and research.

*Source: DLHE

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/business-economics/banking-finance/

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A degree highly respected by quantitative analysts and their employers. About the course. -A highly technical programme for those with strong mathematical skills. Read more
A degree highly respected by quantitative analysts and their employers.

About the course:
-A highly technical programme for those with strong mathematical skills
-Gain knowledge of derivatives pricing tools and methods, as well as the use of programming languages like C++ and VBA
-Designed with the support of industry practitioners to equip students with the skills and knowledge needed to succeed
-Graduates are able to make an early contribution through the unique combination of hands-on, practical skills and the necessary underlying finance theory
-Benefit from the combined expertise of both the ICMA Centre and the Department of Mathematics

COURSE OVERVIEW

The ICMA Centre’s financial engineering degree is highly respected by quantitative analysts and their employers. The credit crunch and subsequent events have emphasised the need to develop better pricing and better hedging models for all complex products. The practical and quantitative skills that you will develop on the programme will equip you to meet this challenge.

Our compulsory modules provide a firm grounding in probability theory, stochastic calculus, derivatives pricing, quantitative and numerical methods, structuring products, volatility analysis, and the modelling of credit, equity, foreign exchange and interest rate derivatives. We also provide a thorough training in C++ and other programming tools.

Optional modules will allow you to focus on risk analysis, portfolio management, designing trading strategies or econometric analysis. This newly structured degree aims to further enhance the strong reputation of its precursor – the MSc in Financial Engineering and Quantitative Analysis, which was established back in 1999. A good background in mathematics is required for acceptance to this programme.

EMPLOYABILITY

Many of our financial engineering graduates are now working as Quants in large London banks and other financial institutions. Others have pursued PhDs and have successful academic careers. Financial instruments are becoming ever more sophisticated, so graduates that understand complex modelling techniques are always in great demand. The high quantitative content of this programme opens many doors to a wide range of careers. You could structure and develop new debt or equity solutions to meet clients funding and hedging needs, or you could become a proprietary trader in exotic derivatives, or a software specialist or a quantitative analyst supporting the traders.

There are excellent opportunities on the buy-side, with hedge funds and investment institutions, as well as in investment banking and in software analytics. Opportunities in quantitative research, or with a rating agency, are among the many other attractive alternatives. Outside of mainstream banking and investment, you might also consider firms involved in commodity and energy trading, or the treasury divisions of leading multinationals and management consultancies.

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This programme provides you with advanced analytical training, quantitative knowledge and the practical skill sets required by modern financial institutions. Read more
This programme provides you with advanced analytical training, quantitative knowledge and the practical skill sets required by modern financial institutions. It aims to equip you with a solid education in financial analysis, risk management and financial engineering for a successful career in the finance and banking industries. It is heavily maths/quant weighted with advanced maths modules and programming modules designed with practical applications in mathematical/quant finance.

The programme will equip you with:
• intellectual skills and theoretical understandings appropriate for the study of financial mathematics and quantitative analysis at postgraduate level
• practical mathematics and object-oriented programming skills linking finance theories to real-world application
• skills in research, evaluation and analysis and the quantitative techniques to evaluate and interpret complex data and research literature
• skills and abilities to devise, plan and undertake complex research projects in the field of financial mathematics

Core Modules

• Advanced Modelling Methods in Finance
• Advanced Financial Econometrics
• Computational Methods in Finance
• Continuous Time Finance
• Advanced Statistics
• Stochastic Calculus
• Dissertation

Elective Modules

• Microeconomics for Financial Mathematics
• Quantitative Methods
• Numerical Computation in Finance
• Advanced Risk Management

What are my career prospects?

A graduate degree in financial mathematics gives you many employment opportunities in the business world such as in banks, investment firms, insurance companies, consulting services to financial industries, government regulators, business entities, and teaching and research at universities or research institution, and government entities.

NOTE: ICAEW ACCREDITATION IS STILL OUTSTANDING. APPLICATION IN PROGRESS.

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This programme is especially suitable for students wishing to gain an in-depth understanding of the field of employment relations as preparation for a career in Employment Relations, Labour Relations or related fields. Read more
This programme is especially suitable for students wishing to gain an in-depth understanding of the field of employment relations as preparation for a career in Employment Relations, Labour Relations or related fields.

In addition to providing students with a thorough grounding in the theory and practice of Employment Relations it is anticipated that on completion of the programme students will also meet the knowledge requirements for chartered membership of the Chartered Institute for Personnel and Development (CIPD), the professional body for HR, Employment Relations and related professions in the UK.

Taught by academics with a strong track record in both Employment Relations related research and practical experience of Employment Relations and HRM, the programme focuses on developing critical thinking and analytical skills alongside of the more practical skills required for a career in Employment Relations and HR.

Core subjects include employment law, developing skills for business leadership, HRM theory and practice, employee engagement, motivation and voice, work design, organisational change and development, wellbeing and work, employment relations, strategic HRM, HRM research methods, and a dissertation.

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/business-economics/employmentrelationsandhrm/

Programme modules

Semester 1:
Compulsory Modules
- Financial Economics
- Research Methods
- Research Communication (two-semester module)
- The Financial System

Optional Modules:
- Economics of Money and Finance
- Macroeconomic Analysis
- Microeconomics Analysis
- Stochastic Models in Finance
- Introduction to Measure Theory and Martingales

Semester 2:
Compulsory Modules
- Asset Management and Derivatives, or Corporate Finance
- Banking and Financial Markets
- Further Quantitative Techniques for Finance and Economics
- Research Communication (two-semester module)

Optional Modules (choose one)
- Applied Banking and Financial Modelling
- Comparative Banking
- Credit Risk Management
- Development Finance
- Stochastic Calculus and Theory of Stochastic Pricing

The School reserves the right to vary the list of optional modules.

Summer:
Students satisfy the research requirement by examined participation in research seminars. Subject to special conditions, students may submit a dissertation instead.

Careers and further study

Most large organisations in both the public and private sectors employ employment relations specialists. The grounding in Employment Relations and UK employment law, in addition to a grounding in more general HRM, that the programme provides also means graduates will be well equipped to bring expertise to both specialist Employment Relations and more general HR and management roles in both private and public sector organisations.

Scholarships and sponsorships

School awards may be available for high-calibre national and international students.

Why choose business and economics at Loughborough?

Loughborough’s School of Business and Economics is a thriving forward-looking centre of education that aims to provide an exceptional learning experience.

Consistently ranked as a Top-10 UK business school by national league tables, our graduates are highly employable and enjoy starting salaries well above the national average.

The rich variety of postgraduate programmes we offer ranges from taught masters, MBA and doctoral programmes, to short courses and executive education, with subjects spanning Management, Marketing, Finance and Economics, Work Psychology, Business Analytics, International Crisis Management and Information Management. New for 2016, we are also launching two exciting new programmes in Human Resource Management. All of this contributes to a lively and supportive learning environment within the School.

- Internationally Accredited
The School of Business and Economics is one of less than 1% of business schools in the world to have achieved accreditation from all three major international accrediting bodies: The Association to Advance Collegiate Schools of Business (AACSB International), EQUIS accreditation from the European Foundation for Management Development (EFMD) and the Association of MBAs (AMBA).

- Career Prospects
Our graduates are in great demand. Over 94% of our postgraduate students were in work and/or further study six months after graduating.* As such, you will be equipped with skills and knowledge that will serve you well in your career or enable you to pursue further study and research.

*Source: DLHE

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/business-economics/employmentrelationsandhrm/

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The Masters Programme aims to develop students’ mathematical and computational skills, and also those in financial modelling. The curriculum includes such subjects as probability theory, stochastic calculus, numerical methods, optimisation and control theory, stochastic finance, interest rate models and credit risk. Read more
The Masters Programme aims to develop students’ mathematical and computational skills, and also those in financial modelling.
The curriculum includes such subjects as probability theory, stochastic calculus, numerical methods, optimisation and control theory, stochastic finance, interest rate models and credit risk. It thus provides a thorough training in modern mathematical finance. In studying for our Masters, students are put in contact with the most important technical and quantitative topics of finance, both theoretical and applied, which range from mathematical background to the latest trends in the financial sector. Increasingly, the financial sector demands a Masters degree in Mathematical Finance from a prestigious university as a prerequisite for recruitment. Our students have often been recruited by prominente companies whilst still preparing their Masters’ thesis, at both a national and na international level. Amongst others, such companies include: EY, Mercer, KPMG, Deloitte, CGD, the Bank of Portugal, BNP Paribas, BPI, Banque Européenne d’Investissement (EIB), Banque Centrale Européenne, Lloyds Bank, and Santander bank. ISEG - Lisbon School of Economics and Management, of ULisboa, has well established departments of Mathematics, Economics and Management, which enables our students to benefit from the consequent synergies, and it provides excellent conditions for hosting the Masters in Mathematical Finance. This fact, together with the high quality of the academic staff of this Masters, all of whom hold PhDs from
prestigious universities (such as the Stockholm School of Economics and the Universities of Oxford, Edinburgh and Barcelona), makes it unique in our country.

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The master of science in computational finance is designed for students interested in computational or quantitative finance careers in banking, finance, and a growing number of additional industries. Read more

Program overview

The master of science in computational finance is designed for students interested in computational or quantitative finance careers in banking, finance, and a growing number of additional industries. Professionals in these fields use their strengths in business, modeling, and data analysis to understand and use complex financial models, often involving differential and stochastic calculus.

The program addresses a vital and growing career field, reaching beyond banking and finance. Typical job titles include risk analyst, research associate, quantitative analyst, quantitative structured credit analyst, credit risk analyst, quantitative investment analyst, quantitative strategist, data analyst, senior data analyst, fixed income quantitative analyst, and financial engineer. Computational finance is an excellent career option for technically-oriented professionals in the fields of business, math, engineering, economics, statistics, and computer science. Programming knowledge is highly preferred.

Plan of study

The curriculum offers an integration of finance, mathematics, and computing. The required mathematics courses have substantial financial content and the experiential computational finance course, which students take during the summer, makes use of skills learned in the mathematics, analytics, and finance courses taken up to that point. The program has a strong multidisciplinary nature and combines the expertise of four of RIT's colleges. The program is a full-time, 17-month curriculum beginning exclusively in the fall. The program ends with a required non-credit comprehensive exam based on the courses completed by the student.

Curriculum

Computational finance, MS degree, typical course sequence:
-Accounting for Decision Makers
-Survey of Finance
-Equity Analysis
-Debt Analysis
-Advanced Derivatives
-Mathematics for Finance I
-Mathematics for Finance II
-Analytics Electives
-Electives
-Computational Finance Experience

Other admission requirements

-Submit official transcripts (in English) from all previously completed undergraduate and graduate course work.
-Submit the results of the Graduate Management Admission Test (GMAT) or Graduate Record Exam (GRE) (GMAT preferred).
-Submit a personal statement (Applicants should explain why their background, please indicate mathematical and programming knowledge, and interests make them suitable for the program).
-Submit a current resume, and complete a graduate application.
-International applicants whose native language is not English must submit scores from the Test of English as a Foreign Language. Minimum scores of 580 (paper-based) or 92 (Internet-based) are required. Scores from the International English Language Testing System (IELTS) will be accepted in place of the TOEFL exam. The minimum acceptable score is 7.0. The TOEFL or IELTS requirement is waived for native speakers of English or for those submitting transcripts from degrees earned at American institutions. For additional information on the IELTS, visit http://www.ielts.org.
-Completed applications for admission should be on file in the Office of Graduate Enrollment Services at least four weeks prior to registration for the next academic semester for students from the United States, and up to 10 weeks prior for international students applying for student visas.
-Accepted students can defer enrollment for up to one year. After one year, a new application must be submitted and will be re-evaluated based on the most current admission standards.

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Programme structure. The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. Read more
Programme structure
The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. There are examinations and coursework in eight modules altogether, including the four core modules. Additionally, all students complete a dissertation.

Core modules
0.Probability and stochastics. This course provides the basics of the probabilistic ideas and mathematical language needed to fully appreciate the modern mathematical theory of finance and its applications. Topics include: measurable spaces, sigma-algebras, filtrations, probability spaces, martingales, continuous-time stochastic processes, Poisson processes, Brownian motion, stochastic integration, Ito calculus, log-normal processes, stochastic differential equations, the Ornstein-Uhlenbeck process.


0.Financial markets. This course is designed to cover basic ideas about financial markets, including market terminology and conventions. Topics include: theory of interest, present value, future value, fixed-income securities, term structure of interest rates, elements of probability theory, mean-variance portfolio theory, the Markowitz model, capital asset pricing model (CAPM), portfolio performance, risk and utility, portfolio choice theorem, risk-neutral pricing, derivatives pricing theory, Cox-Ross-Rubinstein formula for option pricing.


0.Option pricing theory. The key ideas leading to the valuation of options and other important derivatives will be introduced. Topics include: risk-free asset, risky assets, single-period binomial model, option pricing on binomial trees, dynamical equations for price processes in continuous time, Radon-Nikodym process, equivalent martingale measures, Girsanov's theorem, change of measure, martingale representation theorem, self-financing strategy, market completeness, hedge portfolios, replication strategy, option pricing, Black-Scholes formula.


0.Financial computing I. The idea of this course is to enable students to learn how the theory of pricing and hedging can be implemented numerically. Topics include: (i) The Unix/Linux environment, C/C++ programming: types, decisions, loops, functions, arrays, pointers, strings, files, dynamic memory, preprocessor; (ii) data structures: lists and trees; (iii) introduction to parallel (multi-core, shared memory) computing: open MP constructs; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.


0.Interest rate theory. An in-depth analysis of interest-rate modelling and derivative pricing will be presented. Topics include: interest rate markets, discount bonds, the short rate, forward rates, swap rates, yields, the Vasicek model, the Hull-White model, the Heath-Jarrow-Merton formalism, the market model, bond option pricing in the Vasicek model, the positive interest framework, option and swaption pricing in the Flesaker-Hughston model.

Elective modules

0.Portfolio theory. The general theory of financial portfolio based on utility theory will be introduced in this module. Topics include: utility functions, risk aversion, the St Petersburg paradox, convex dual functions, dynamic asset pricing, expectation, forecast and valuation, portfolio optimisation under budget constraints, wealth consumption, growth versus income.


0.Information in finance with application to credit risk management. An innovative and intuitive approach to asset pricing, based on the modelling of the flow of information in financial markets, will be introduced in this module. Topics include: information-based asset pricing – a new paradigm for financial risk management; modelling frameworks for cash flows and market information; applications to credit risk modelling, defaultable discount bond dynamics, the pricing and hedging of credit-risky derivatives such as credit default swaps (CDS), asset dependencies and correlation modelling, and the origin of stochastic volatility.

0.Mathematical theory of dynamic asset pricing. Financial modelling and risk management involve not only the valuation and hedging of various assets and their positions, but also the problem of asset allocation. The traditional approach of risk-neutral valuation treats the problem of valuation and hedging, but is limited when it comes to understanding asset returns and the behaviour of asset prices in the real-world 'physical' probability measure. The pricing kernel approach, however, treats these different aspects of financial modelling in a unified and coherent manner. This module introduces in detail the techniques of pricing kernel methodologies, and its applications to interest-rete modelling, foreign exchange market, and inflation-linked products. Another application concerns the modelling of financial markets where prices admit jumps. In this case, the relation between risk, risk aversion, and return is obscured in traditional approaches, but is made clear in the pricing kernel method. The module also covers the introduction to the theory of Lévy processes for jumps and its applications to dynamic asset pricing in the modern setting.

0.Financial computing II: High performance computing. In this parallel-computing module students will learn how to harness the power of a multi-core computer and Open MP to speed up a task by running it in parallel. Topics include: shared and distributed memory concepts; Message Passing and introduction to MPI constructs; communications models, applications and pitfalls; open MP within MPI; introduction to Graphics Processors; GPU computing and the CUDA programming model; CUDA within MPI; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.


0.Risk measures, preference and portfolio choice. The idea of this module is to enable students to learn a variety of statistical techniques that will be useful in various practical applications in investment banks and hedge funds. Topics include: probability and statistical models, models for return distributions, financial time series, stationary processes, estimation of AR processes, portfolio regression, least square estimation, value-at-risk, coherent risk measures, GARCH models, non-parametric regression and splines.

Research project

Towards the end of the Spring Term, students will choose a topic to work on, which will lead to the preparation of an MSc dissertation. This can be thought of as a mini research project. The project supervisor will usually be a member of the financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

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