This MSc Financial Mathematics will equip you with the mathematical and computational skills required in the finance and insurance industries.
This programme is also an excellent training ground for students wishing to embark upon a research degree in financial or actuarial mathematics.
Introduction
Mathematical Sciences at Liverpool provides a centre for world class research and teaching across many areas and at the leading edge of the subject.Our teaching was evaluated as ‘excellent’ by the Quality Assurance Agency in its most recent survey and awarded 23 points out of a possible 24.
We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable. We provide high quality supervision, teaching and IT support and you will benefit from the friendly and supportive atmosphere in the Department.
This programme is available to full-time students only. In each semester (semester one and semester two) students take four compulsory modules (15 credits each). The programme finishes with a summer dissertation written under the supervision of a member of staff (60 credits).
This programme is ideal for professionals with mathematical background who would like to start, or further develop a specific career in the finance and insurance industries.
What you'll learn
Probability theory
Stochastic analysis and mathematical modelling
Computational methods
Financial derivatives
Risk management
Econometrics.
Course content
Discover what you'll learn, what you'll study, and how you'll be taught and assessed.
Semester one
In Semester One students take four compulsory modules (15 credits each).
Compulsory modules
ECONOMETRIC AND STATISTICAL METHODS (ECON814)
Credits: 15 /
Semester: semester 1
Econometric and statistical methods are of vital importance for estimating relationships between economic and financial variables, and for making predictions about the future. Central banks maintain large scale forecasting models for macroeconomic variables, for instance, and policy institutes use a wide range of econometric tools for modeling macroeconomic or microeconomic data. Within the private sector, financial analysts routinely estimate volatility models, credit risk departments estimate probability of default models, and, as a final example, marketing departments in large e-businesses make use of website hit counts and treatment test methods to test for the effect of their promotions on demand. These are just a few examples of how relatively advanced econometric methods are used in practice. ECON814 Econometric and Statistical Methods lays the foundation for learning the more specialised methods taught in ECON920 Advanced Econometrics, and equips the participant with a good general understanding of the methods used for estimating and testing linear and nonlinear relationships between variables.
PROBABILITY ESSENTIALS FOR FINANCIAL CALCULUS (MATH480)
Credits: 15 /
Semester: semester 1
Modelling and valuation of financial derivatives (options etc.) uses stochastic analysis and concepts from modern probability theory, in particular probability sigma-algebras, measures, expectation as Lebesgue integral, conditional expectations, filtrations and martingales. This module provides students with an introduction to these concepts. It is essential for study of stochastic analysis and continuous time models for pricing financial derivatives.
STOCHASTIC MODELLING IN FINANCE (MATH482)
Credits: 15 /
Semester: semester 1
This module demonstrates the advanced mathematical techniques underlying financial markets and the practical use of financial derivative products to analyse various problems arising in financial markets. Emphases are on various option pricing formulae, hedging methods, and stochastic analysis.
Game Theory with Applications (ECON813)
Credits: 15 /
Semester: semester 1
Game theory studies strategic decision-making that is situations where the outcome does not only depend on your own actions but also that of others. It has significantly changed how business strategists, economists, and policymakers think about problem-solving and has become an indispensable tool in economic modelling, strategy analysis, and negotiation techniques. As strategic decision-making arises naturally in many contexts, game theory has influenced many other fields, such as political sciences, biology, and computer sciences. In this module, core concepts and ideas will be illustrated with the help of many everyday examples and economic and business applications, ranging from how groceries are priced to trade wars and political conflicts. This module will boost your strategic thinking to become a successful manager or influential policymaker.
Programme details and modules listed are illustrative only and subject to change.
Semester two
In Semester Two, students take three compulsory and one optional module below (15 credits each).
Compulsory modules
FINANCIAL AND ACTUARIAL MODELLING IN R (MATH377)
Credits: 15 /
Semester: semester 2
This module focuses on the applications of actuarial and financial mathematics using the programming language R. It provides the students with an introduction to the basic principles of programming in R. Students will practice various computational aspects of actuarial science and finance. The module focuses on the implementation of the theoretical models, learned in other modules, using R code. Students will develop a background in the practical applications of Statistics, Reserving, Portfolio management, Option pricing, and others. This module will enhance the employability skills for students in Financial and Actuarial Mathematics.
INTEREST RATE THEORY (MATH481)
Credits: 15 /
Semester: semester 2
The main purpose of this module is to present methods for pricing various contracts in a stochastic interest rate setting, using both the risk-neutral pricing approach and the partial differential equations approach. The pricing of the following contracts are considered in detail: zero-coupon bonds, forward contracts, European options, swaps, caps, floors, and swaptions. The module is based on the results from probability theory and stochastic analysis.
STOCHASTIC ANALYSIS AND ITS APPLICATIONS (MATH483)
Credits: 15 /
Semester: semester 2
This module provides the foundations of stochastic analysis. Many of the basic results are considered in detail, in particular the ones that play a crucial role in applications such as mathematical finance. Students taking this module will study conditional expectations, martingales, Brownian motion, Brownian bridge, the reflection principle and scaling, stopping times, Ito’s integral and stochastic calculus, stochastic differential equations (linear and nonlinear), martingale representation, Girsanov theorem, and Feynman-Kac formula. Applications include stochastic control, optimal investment, and mathematical finance. All the theoretical results are illustrated with numerical examples from various fields of applications.
Optional modules
Applied Macroeconometrics (ECON920)
Credits: 15 /
Semester: semester 2
This module will provide students with an understanding of modern econometric time series methodology suitable for applications to financial and macroeconomic data. Topics include model selection, estimation and forecasting for univariate models; nonstationary models and testing for nonstationarity; models with conditional heteroscedasticity; and model selection, estimation and forecasting for multivariate models and testing for cointegration.
MATHEMATICAL RISK THEORY (MATH366)
Credits: 15 /
Semester: semester 2
To provide an understanding of the mathematical risk theory used in practise in non-life actuarial depts of insurance firms, to provide an introduction to mathematical methods for managing the risk in insurance and finance (calculation of risk measures/quantities), to develop skills of calculating the ruin probability and the total claim amount distribution in some non ‐ life actuarial risk models with applications to insurance industry, to prepare the students adequately and to develop their skills in order to be exempted for the exams of CT6 subject of the Institute of Actuaries (MATH366 covers 50% of CT6 in much more depth).
Programme details and modules listed are illustrative only and subject to change.
Final project
The main Dissertation gives you the opportunity to study a subject of your choice related to your specialist area, and to show an ability to integrate theories and concepts drawn from the wider mathematics, business and management literature with use of empirical case studies, empirical work, or references to appropriate empirical work. Students taking MATH554 will develop expertise in their chosen area, and techniques which will improve their research skills in problem definition, information collection, analysis, synthesis, reasoned argument, individual initiative and judgement. Students will also have the opportunity to develop their communication skills, including technical writing. (60 credits).
Optional modules
MAIN DISSERTATION (MATH554)
Credits: 60 /
Semester: summer
This is your opportunity to study in depth a mathematical topic which interests you, and produce a substantial written report upon it. Your supervisor will help you select a suitable topic, and guide you in your studies and writing. For some students this is a prelude to embarking on a research degree, and for others it is an end in its own right, but for all it should be both stimulating and exciting.
Programme details and modules listed are illustrative only and subject to change.
How you'll learn
The delivery of the ‘MATH’ modules is through classroom lectures and tutorials. These are in-person and on campus. There are 12 weeks of teaching in each semester, after which the students take their final assessment. There are 4 hours per module each week. All the teaching material is available to the students through canvas, and this includes lecture notes and solutions to tutorials.
Some lectured modules use a ‘traditional’ format, with lectures supported by tutorials. Others use a hybrid approach, with some online content and interactive face to face classes. Your lecturers will provide details of the format for their modules at the start of each semester. The research groups in the department have regular seminars. These are currently operating in a hybrid format, with some seminars delivered in person and some online. MSc students are expected to attend seminars throughout the year, right from the beginning of the course. They may be difficult to understand at first, but you will find that they become much clearer as the year progresses. Attending will give you an opportunity to see what is happening at research level, and to have regular contact with people in the relevant area.
We are proud of our record on teaching quality, with many of our MSc modules delivered by world-leading experts. Five members of the Department have received the prestigious Sir Alastair Pilkington Award for Teaching. Our staff use a range of teaching methods, including traditional ‘chalk and talk’ delivery, stream captured lectures using tablets, pencasts and online assessment and feedback. The Mathematics Centre for Enhancement in Education helps staff to develop innovative techniques for teaching mathematics.
How you're assessed
All taught ‘MATH’ modules, this academic year, have a continuous assessment (CA) component and the final assessment (FA) component. The FA component is taken in January and May exam periods. These, together with ‘ECON’ modules, constitute 120 credits of the programme. There is a summer dissertation which constitutes the remaining 60 credits of the programme. The students work on the dissertation from June to mid-September. The students can choose a topic to work on from a number of topics offered by the members of IFAM (Institute of Financial and Actuarial Mathematics).
Liverpool Hallmarks
We have a distinctive approach to education, the Liverpool Curriculum Framework, which focuses on research-connected teaching, active learning, and authentic assessment to ensure our students graduate as digitally fluent and confident global citizens.
Course options
Studying with us means you can tailor your degree to suit you. Here's what is available on this course.
We offer a very wide range of optional modules, allowing students to specialise in pure mathematics, applied mathematics or theoretical physics. This allows you to build up the required background for the project and dissertation modules, which offer the opportunity to undertake an in-depth study of a topic of your choice, supervised by a leading expert in the field. Find out more on our departments webpage here.
Support for students with differing needs from the Disability advice and guidance team. They can identify and recommend appropriate support provisions for you.
What students say...
The whole experience has been amazing, and it has helped me grow professionally and personally. The thing I enjoyed most is the fact that I was able to meet a lot of people from different cultures and backgrounds coming from every part of the world. This is something that strongly enriched me, and I am grateful for all the amazing people that I can actually call my friends.
The MSc programme is of course a natural route into doctoral study in Mathematics and related fields. Some of our PhD students move on to postdoctoral positions and to academic teaching jobs and jobs in research institutes, both in the UK and elsewhere.
Recent graduates have moved into fast track teacher programmes, jobs in finance (actuarial, banking, insurance), software development, drugs testing and defence work, as well as University postdoctoral or lecturing posts.
Career support from day one to graduation and beyond
Upon successful completion of the degree you will be ideally equipped to work in:
investment banks
pension or investment funds
hedge funds
consultancy and auditing firms or government regulators.
Fees and funding
Your tuition fees, funding your studies, and other costs to consider.
Tuition fees
UK fees (applies to Channel Islands, Isle of Man and Republic of Ireland)
Full-time place, per year
£12,400
International fees
Full-time place, per year
£28,000
Fees stated are for the 2024-25 academic year.
Tuition fees cover the cost of your teaching and assessment, operating facilities such as libraries, IT equipment, and access to academic and personal support.
If you're a UK national, or have settled status in the UK, you may be eligible to apply for a Postgraduate Loan worth up to £12,167 to help with course fees and living costs. Learn more about paying for your studies..
Additional costs
We understand that budgeting for your time at university is important, and we want to make sure you understand any course-related costs that are not covered by your tuition fee. This could include buying a laptop, books, or stationery.
The qualifications and exam results you'll need to apply for this course.
This is a challenging programme so you’ll need a good first degree (2:1 Hons or equivalent) in Mathematics, Mathematical Sciences, Financial Mathematics, Computer Science, Engineering or a subject with substantial mathematical content.
You should have taken modules in Calculus, Linear Algebra, Probability and Statistics at an undergraduate level previously. It is also highly desirable to have knowledge of Differential Equations, Real and Complex Analysis, Numerical Methods, Operations Research, Portfolio Theory, Risk Management and Stochastic Processes.
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Change it here
If you hold a bachelor’s degree or equivalent, but don’t meet our entry requirements, a Pre-Master’s can help you gain a place. This specialist preparation course for postgraduate study is offered on campus at the University of Liverpool International College, in partnership with Kaplan International Pathways. Although there’s no direct Pre-Master’s route to this MSc, completing a Pre-Master’s pathway can guarantee you a place on many other postgraduate courses at The University of Liverpool.
International applicants who do not meet the minimum required standard of English language can complete one of our Pre-Sessional English courses to achieve the required level.
English language qualification
Requirements
IELTS
6.5 overall, with no component below 5.5
TOEFL iBT
88 overall, with minimum scores of listening 17, writing 17, reading 17, and speaking 19
Duolingo English Test
120 overall, with no component below 95
Pearson PTE Academic
61 overall, with no component below 59
LanguageCert Academic
70 overall, with no skill below 60
PSI Skills for English
B2 Pass with Merit overall and no band below B2 Pass
INDIA Standard XII
National Curriculum (CBSE/ISC) - 75% and above in English. Accepted State Boards - 80% and above in English.
WAEC
C6 or above
PRE-SESSIONAL ENGLISH
Do you need to complete a Pre-Sessional English course to meet the English language requirements for this course?
The length of Pre-Sessional English course you’ll need to take depends on your current level of English language ability.
Liverpool bursts with diversity and creativity which makes it ideal for you to undertake your postgraduate studies and access various opportunities for you and your family.
To fully immerse yourself in the university experience living in halls will keep you close to campus where you can always meet new people. Find your home away from home.
Discover what expenses are covered by the cost of your tuition fees and other finance-related information you may need regarding your studies at Liverpool.
Contact us
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