Prospective students

Theoretical modules

Candidates reading for the MSc in Mathematics and Finance follow seven compulsory core modules, and choose another five from a menu of elective modules divided into three indicative streams: Derivatives Pricing, Market Microstructure and Machine Learning in Finance that are offered in autumn and spring terms. The modules cover fundamental mathematics, finance and economic background, scientific computing and statistical methodology. The summer period is devoted to the project.

Project and placements

• A supervised thesis project takes place during the summer months after the theoretical modules have been completed.
• Students who have achieved an acceptable level of academic competence will be offered as candidates to external sponsors.
• These industry-based placements take place in banks, consultancies, hedge funds, insurance companies, rating agencies, or financial software companies.
• Each project is normally based on new areas of possible interest to the sponsor, or extensions to existing lines of work.
• An academic supervisor and the sponsor work with the student to scope out the project at the start; supervision is a joint activity between the former two.
• Undertaking the project on site gives students a genuine insight into the reality of the financial marketplace.

Computing for Finance (Python and C++)

We regard it as essential that students become proficient in object-oriented programming. The computing environment at the college is based on wireless networking. Students must equip themselves, at their own expense, with a laptop running Windows. We will supply the software you need: Microsoft Visual Studio, Microsoft Office and Matlab, a software environment for scientific computing. The teaching in programming stretches over the autumn and spring terms and consists of lectures, laboratory sessions and a series of graded exercises which must be submitted.

Recommended reading and further information

To find out more about the course, including pre-course reading course handbooks, timetables, information on careers support offered and social events, please see the current student pages.

The MSc in Mathematics and Finance can be taken on a part-time basis. Students attend the same lectures as those taking the degree full-time. The courses are spread more or less evenly over two years, instead of one, and the project is taken in the second year. There is a need to attend lectures on about three days a week. Considerable flexibility is needed by those in full-time employment who pursue this option. A typical sample schedule would look like this:

Year 1

Autumn Term

• Stochastic Processes
• Introduction to Option Pricing 
• Computing for Finance - Python
• Electives, from the list of Elective Modules

Spring Term

• Simulation Methods for Finance
• Computing for Finance - C++ 
• Electives, from the list of Elective Modules

Year 2 

Autumn Term

• Statistical Methods in Finance
• Quantitative Risk Management
• Electives, from the list of Elective Modules

Spring Term

• Interest Rate Modelling
• Electives, from the list of Elective Modules

Summer Period

• MSc Project

Graduate destinations

• What do alumni from the MSc in Mathematical Finance go on to do?

Career support

• Practitioners' Lecture Series
• Careers in Quantitative Finance lecture series
• Imperial College Career Services
• Early Career Researcher Institute (ECRI)
• Imperial Horizons

Networks

• Alumni network and events
• Imperial College Finance Society (ICFS)

Topics in Derivatives Pricing: MATH70121

Option markets are extremely diverse, spanning several different asset classes and many pricing and hedging strategies. The goal of this module is to complement the other option-flavoured modules, focusing on the specificities of Foreign Exchange and Fixed Income markets. For each of these markets, the module will study their specific characteristics and evolutions, develop the technical tools needed to understand the pricing of derivatives, and explain how to set up trading and hedging strategies therein. A strong emphasis will be given on the actual implementation of the models and their calibration to real data.

Selected Topics in Quantitative Finance: MATH70128 

Derivatives pricing is the core area quantitative finance which is relevant to various roles in the industry such as quant, trader, structurer and risk manager. The goal of this module is to introduce the required theoretical tools to understand the pricing and hedging of different financial derivatives.

While the exposition of the topics will be done in a theoretical manner, the module will also emphasise on the practical aspects of derivatives trading (e.g. pricing of structured products traded in real life, backtesting of hedging strategies via numerical studies, etc).

Numerical Methods: MATH70119 

The goal of this module is to complement the Core module on Simulation Methods to investigate other techniques that are widely spread among the financial industry. We shall investigate two popular techniques, namely PDE methods and Fourier methods.

For each approach, we will start with a theoretical framework, explaining how an option pricing problem can be turned into a dynamic programming problem, a PDE or a Fourier integration. We shall then focus on the numerical methods to solve these problems. Practical implementations on real models/data will be emphasised.

Optimisation in Machine Learning: MATH70122 

The module covers both the theoretical underpinnings of convex optimisation and its applications to important problems in mathematical finance. A brief outline of the course reads as follows:

• Fundamental properties of convex sets and convex functions
• The basics of optimisation with special emphasis on duality theory
• Markowitz portfolio theory and the CAPM model
• Expected utility maximisation and no arbitrage
• Convexity in continuous time hedging

Stochastic Control in Finance: MATH70126 

Many problems in mathematical finance (and in other areas) are essentially optimisation problems subject to random perturbations, where some controls play the role of a performance criterion. The goal of this module is to bring the main concepts and techniques from dynamic stochastic optimisation and stochastic control theory to the realm of quantitative finance. It will therefore naturally start with a theoretical part focusing on required elements of stochastic analysis, and with a motivation through several examples of control problems in Finance. We will then turn to the classical PDE approach of dynamic programming, including controlled diffusion processes, dynamic programming principle, the Hamilton-Jacobi-Bellman equation and its verification theorem. We will finally see how to derive an solve dynamic programming equations for various financial problems such as the Merton portfolio problem, pricing under transaction costs, super-replication with portfolio constraints, and target reachability problems.

Quantitative Trading and Price Impact: MATH70127 

The increase in computer power over the last decades has given rise to prices being quoted and stocks being traded at an ever-increasing pace. Since humans are not able to place orders at this speed, algorithms have replaced classical traders to optimise portfolios and investments. In this module, we will study specificities of this market, and in particular, we shall develop the mathematical tools required to develop such algorithms in this high-frequency framework. The module will start with a short review of stochastic optimal control, which forms the mathematical background. We shall then move on to study optimal execution, namely how and when to place buy/sell orders in this market, both assuming continuous trading and in the context of limit and market orders. The last part of the module will be dedicated to the concept of market making and statistical arbitrage in high-frequency settings. 

Market Microstructure: MATH70125 

The goal of the module is to develop thorough understanding of how form, information is aggregated, and trades occur in financial markets. The main market types will be described as well as traders’ main motives for why they trade. Market manipulation and high-frequency trading strategies have received a lot of attention in the press recently, so the module will illustrate them and examine recent developments in regulations that aim to limit them. Liquidity is a key theme in market microstructure, and the students will learn how to measure it and to recognise the recent increase in liquidity fragmentation and hidden, “dark” liquidity. The Flash Crash of 6 May 2010 will be analysed as a case study of sudden loss of liquidity.

Portfolio Management: MATH70129 

This module gives students a foundation for quantitative portfolio management and for understanding market price determination. Key concepts include risk measurement, risk-reward trade-offs, portfolio optimization, benchmarking, equilibrium asset pricing, market efficiency, and pricing anomalies. Specific portfolio management tools include mean-variance optimization, CAPM and APT asset pricing, factor models (e.g., Fama-French), momentum strategies, and performance evaluation. The course will present essential theories and formulas and will also review important institutional and empirical facts about equity, bond, and commodity markets.

Reinforcement Learning: MATH70120

The module introduces the latest advances in machine learning. We start with reinforcement learning and demonstrate how it can be combined with neural networks in deep reinforcement learning, which has achieved spectacular results in recent years, such as outplaying the human champion at Go. We also demonstrate how advanced neural networks and tree-based methods, such as decision trees and random forests, can be used for forecasting financial time series and generating alpha. We explain how these advances are related to Bayesian methods, such as particle filtering and Markov chain Monte Carlo. We apply these methods to set up a profitable algorithmic trading venture in cryptocurrencies using Python and kdb+/q (a top technology for electronic trading) along the way.

Deep Learning: MATH70116 

Deep learning is subfield of Machine Learning that applies deep neural nets to represent and predict complex data. It has recently revolutionised several areas such as image recognition and artificial intelligence and it is currently gaining traction also in the financial industry. The module will first introduce the multi-layer neural nets and explain their universal approximation property. Subsequently, the module proceeds to the training of neural nets, starting from the derivation of the gradient of a neural net and its evaluation through backpropagation, culminating in the stochastic gradient descent and related modern optimisation methods. Techniques to avoid overfitting in training are also elucidated. The remainder of the module focuses on the practical implementation and training of deep neural nets using Keras and TensorFlow, with examples in computational and statistical finance. Time permitting, elements of recurrent neural nets are also sketched.

Quantum Machine Learning 

Quantitative Finance is a rapidly changing environment, and the financial industry is always on the lookout for new techniques and new technologies able to harness the rise of big data and the availability of computing power. Quantum computing, though not a recent field, has gained huge popularity in the past few years with the development of small-scale quantum computers and quantum annealers. These have in turn pushed for new algorithms, hybrid between classical and quantum, and tailored for such computers. The financial industry is now looking at such developments and there is a common agreement that this will be one of the leading advances in the coming decade.

 The goal of this new Elective (so far not given in any similar MSc programmes around the world) is to introduce students to this new technology and these new algorithms and show them how they can be used to solve financial problems, in particular

• For portfolio optimisation,
• For data generation,
• For Machine learning and neural network.

The module will strike a fair balance between theoretical concepts of Quantum Computing, their implementation (in Python using IBM’s Qiskit framework) and their application to real financial problems. 

Generative Modelling in Finance MATH70xxx

The goal of this module is to present the most widely used generative AI algorithms: denoising diffusion models, flow matching and related variants such as neural stochastic differential equations. These models are all based on differential equations and are the backbone of the best image, audio, and video generation models (e.g., Stable Diffusion 3 and Movie Gen Video). In addition they have most recently became the state-of-the art in scientific applications such as protein structures (e.g., AlphaFold3 is a diffusion model).

At the end of the module students will be able to: 1) Understand the mathematical underpinnings behind recent state-of-the art generative models; 2) Understand how classical ODE and SDE theory can be integrated with modern deep learning tools; 3) Implement their own diffusion model from scratch and apply it to real world examples.

 Jordan Anaya (MSc Mathematics and Finance 2018-2019)

Quant Analyst at Velador Associates, a data science firm specialized in financial litigation services

Why did you choose the MSc in Mathematics and Finance at Imperial College?

After 4 years working as Derivatives Pricing and Accounting consultant I decided I wanted to deepen my knowledge in some areas of Mathematics and Finance that I did not cover in my undergrad and that would help me go further in my career. I chose the MSc at Imperial as it is one of the best in the world with the latest research topics in the industry and with the Elective modules that allow you to tailor the course on the topics you are most interested.

What did you enjoy most during the MSc?

I enjoyed a lot the Practitioners' Lectures as they share with you their latest research on topics applied in practice, as well as the opportunity to do the thesis project with an external supervisor from the industry. 

What do you think are the strongest points of the MSc?

The lecturers are amazing, they engage with the students throughout the lectures, and you can notice their passion and in-depth knowledge. On top of that they are part of one of the world's leading research groups in Mathematics and Finance and they are always helpful if you approach them. Also, the focus of the Masters in coding helps you improve your skills which is very useful in practice.

What piece of advice would you give to anyone thinking of applying to the programme?

Do some study before the Masters as it is a course from which you learn a lot but you have to review a large quantity of information for the exams. Practice to improve your coding skills as you will use it for the projects and will make them easier.

Cécilia Auburn (MSc Mathematics and Finance 2019-2020)

PhD student with the Econophysics Chaire in Polytechnique Paris, working on endogeneous liquidity crisis

Why did you choose the MSc in Mathematics and Finance at Imperial College?

When looking at quant job offers from hedge funds or banks, they ask for many different skills and the MSc Mathematics and Finance of Imperial tackles all of those, with a bonus: it is well connected with the financial industry.

What did you enjoy most during the MSc?

I really enjoyed the Careers meetings. First, there are food and drinks! But mostly, we get to meet HR, Quants, and have a privileged contact with them to discuss about their jobs and the recruitment processes. It is also a great moment to share with the other MSc students!

What do you think are the strongest points of the MSc?

Probably, the availability of its people. It is really easy to get a meeting to discuss or ask questions with anyone of the MSc programme. It is really helpful.

What piece of advice would you give to anyone thinking of applying to the programme?

Take part in as many MSc events you can, there are plenty of opportunities, you do not want to miss them!

Elisa Barbaro (MSc Mathematics and Finance 2013-2014)

Exotics trader at Citigroup

 Why did you choose the MSc in Mathematics and Finance at Imperial College?

The teaching quality had good reputation and at the same time I thought it would help me bridge the gap between academia and work (because of the work placement project and being in London).

What did you enjoy most during the MSc?

The work placement project.

What do you think are the strongest points of the MSc?

I think it can vary. In my case, during my BSc, I studied mainly the more theoretical aspects of Maths/Engineering, because in Italy (except for a couple of Business Schools) students don’t usually get taught how to apply for a job or what opportunities one can look for. The strongest point in my view was to bridge this gap between academia and work (especially in finance). I remember other students didn’t know how to code and the course helped them for that, which is also important. It depends on each individual situation. 

What piece of advice would you give to anyone thinking of applying to the programme?

The course provides you with a lot of information and events, across a wide range of topics. You will not achieve in-depth knowledge on any specific topic, but likely, you don’t need it, as it is more important to know what various subjects involve and what ultimately you like to pursue. You might not learn enough concepts to interview for jobs as a hardcore quant, but I think many students start their career thinking that they want to be a quant to then discover that they prefer other roles, and this course gives you the chance to apply to most jobs out there. You can also continue to study more and still be a hardcore quant some years later!

George Lambert (MSc Mathematics and Finance 2012-2013)

Founder of Lambert Labs, a Python-focused software development agency based just around the corner from Imperial in Earls Court. We build software solutions for companies ranging in size from start-ups all the way through to global corporations. Our solutions are very much cross-industry too; we have clients in the education, finance, legal, hospitality and logistics sectors.

Why did you choose the MSc in Mathematics and Finance at Imperial College?

I worked as a secondary school Maths teacher for three years after doing a Maths undergraduate degree but was looking for a way to combine my academic/career experience in Maths with a passion for technology and an interest in Finance. Training for a career as a quant seemed like the natural choice and after researching similar courses at various UK and international universities, I decided that the MSc in Mathematics and Finance at Imperial looked like the perfect course for me. 

What did you enjoy most during the MSc?

As part of the MSc I did a project internship at Citigroup over the summer. This gave me exposure to how quantitative methods are used in industry on a day-to-day basis. This exposure was absolutely invaluable at the time, and led to getting a part-time job Junior Quantitative Analyst role at Citigroup while studying part-time for a PhD at Imperial (unfortunately a serious sports injury put a stop to this role and the PhD at a later date!).

What do you think are the strongest points of the MSc?

There isn’t one single thing that I want to put my finger on and say, ‘this area was the strongest’. However, the course as a whole was excellent. There is no doubt in my mind that I learnt more in my year on the MSc than i any other year in my life. The combination of lectures, office hours, exams, library study, coursework and research projects is intense, but extremely valuable.

What piece of advice would you give to anyone thinking of applying to the programme? 

Do as much research as possible before applying. This could involve reading about Mathematics and Finance in academia or Mathematics and Finance in industry, or both. If you are accepted onto the programme and haven’t coded before, it is a good idea to learn some programming basics before you start the course, just so you can hit the ground running!

Aitor Muguruza (MSc Mathematics and Finance 2015-2016)

 Head of Quant Modelling at a Hedge Fund

Why did you choose the MSc in Mathematics and Finance at Imperial College?

Among the different choices in the EU and UK, London is probably the strongest Quant Hub in the continent. Imperial offered the best curriculum and the best job market.

What did you enjoy most during the MSc?

I enjoyed the balance and depth on both numerical and theoretical courses.

What do you think are the strongest points of the MSc?

A constantly updated curriculum that is always on top of the market requirements. When I did my MSc few years ago, Python was picking up in the industry which I had already been exposed to through different modules in the course. The same story applies to Machine Learning courses and other topics, it's not just about basics also what is currently relevant.

What piece of advice would you give to anyone thinking of applying to the programme?

I would say there is a lot to learn to be a Quant, a lot of asset classes, diverse roles in different technology areas. I believe it is helpful to start narrowing down what your ideal role is, to be able to make the most of the MSc in terms of elective modules. This does not mean that by day 1 you should know what you are aiming at, but it is certainly important to do some market research before and during the first term.

Niklas Walter (MSc Mathematics and Finance 2019-2020)

PhD student in Financial Mathematics at the University of Munich in Germany focusing on rough volatility

Why did you choose the MSc in Mathematics and Finance at Imperial College?

I think that the programme at Imperial perfectly combines academic excellence and the opportunity to get insights about how the taught knowledge is in fact applied in the industry. Moreover, the university’s location in the heart of Europe’s centre of the financial industry is a daily motivation to learn new things.

What did you enjoy most during the MSc?

I think one of the most important aspects of the programme is the social one. Studying together with a very international cohort is quite enrichened and interesting. Moreover, the entire staff of Imperial and in particular of the MSc is very motivating and supportive. Lastly, the weekly Career events followed by some more casual pub visits are helpful to start building a professional network and to gain interesting insides about current topics driving the quant world. 

What do you think are the strongest points of the MSc?

At first, I want to mention the weekly Career events again. They are indeed very well organised and a good opportunity to find an industry partner for one’s final project. In addition, the range of Elective courses is quite broad and oriented towards the current needs and topics in the industry. Lastly, the programme offers a good blend between pure mathematical techniques and their real-world applications.

What piece of advice would you give to anyone thinking of applying to the programme?

One advice is to reach out to former students to get a better impression of the programme. In general, it is important to carefully look at the programme structure and course contents to get a clear idea about why you want to apply and if it is even the right MSc for you.

Read answers to our frequently asked questions from prospective students.

• Frequently asked questions