Our course finder pages contain all the most up-to-date information about the Financial Mathematics and Machine Learning MSc, including details of the programme structure, compulsory and elective modules and study options.
Click here to see the full MSc Financial Mathematics and Machine Learning programme structure.
Below is a full list of all modules which we expect to be available to students on this programme across the semesters. Please note that this list, and the contents of the individual modules, is for information only and may be subject to change.
This module covers the advanced programming techniques in C++ that are widely used by professional software engineers and quantitative analysts & developers. The most important of these techniques is object-oriented programming, embracing the concepts of encapsulation, inheritance and polymorphism. We then use these techniques to price a wide range of financial derivatives numerically, using several different pricing models and numerical methods. On completion of this module, you will have acquired the key skills needed to apply for your first role as a junior ‘quant’ or software developer in a financial institution.
This module covers a number of advanced topics in the pricing and risk-management of various types of derivative securities that are of key importance in today's financial markets. In particular, the module covers models for interest rate derivatives (short-rate and forward-curve models), and looks at the multi-curve framework. It then considers credit risk management and credit derivatives (both vanilla and exotic). Finally, it also discusses credit valuation adjustment (CVA) and related concepts.
This module is offered to allow you to move beyond the basic techniques of Machine Learning. Together with the initial module (Machine Learning with Python), this course will provide a comprehensive overview of Machine Learning and its mathematical foundations as well as an introduction to the current state of the art in the field.
The aim of this module is to introduce students to more advanced machine learning techniques. An emphasis will be on current techniques which are relevant for practical applications. In addition to practical programming assignments, the course will also give you an understanding of the mathematical underpinning of the techniques and the limitations of the methods which are crucial to correctly assessing their performance.
Building on the module in semester A, linear methods will be extended to non-linear settings using kernel methods. The module will also go further in depth with topics which were introduced in the first semester such as neural networks and Monte Carlo Markov Chain methods (MCMC). It will cover specific applications and provide students with an overview of the current state of the art techniques.
This module explains how we can price financial derivatives in a consistent manner, in the realistic case where the price of the underlying asset changes continuously in time. To do this, we first introduce the key ideas of stochastic calculus in a mathematically rigorous, but still accessible, way. Then, using the Black-Scholes model, we show how we can price a wide range of derivatives, using both the PDE approach and the alternative martingale approach. Finally we look at several more recent models that attempt to rectify some of the known deficiencies of the Black-Scholes model.
This module first introduces you to various types of financial instruments, such as bonds and equities, and the markets in which they are traded. We then explain in detail what financial derivatives are, and how they can be used for hedging and speculation. We also look at how investors can construct optimal portfolios of assets by balancing risk and return in an appropriate way. This module will give you the practical knowledge that is essential for a career in investment banking or financial markets.
The project component of the MSc programme will give you the opportunity to undertake some significant and advanced study in an area of interest, under the guidance of an expert in that field. Many projects involve a substantial amount of programming and analysis. Your project will be assessed by a written dissertation (of up to 60 pages) which you will submit in early September.
Possible project topics may include:
This module introduces you to all of the fundamental concepts needed for your future studies in financial mathematics. After reviewing some key ideas from probability theory, we give an overview of some of the most important financial instruments, including shares, forward contracts and options. We next explain how derivative securities can be priced using the principle of no arbitrage. Various models for pricing options are then considered in detail, including the discrete-time binomial model and the continuous-time Black-Scholes model.
This module aims to provide students with Machine Learning skills based on the Python programming language as it is currently used in industry. Some of the presented methods are regression and classification techniques (linear and logistic regression, least-square); clustering; dimensionality reduction techniques such as PCA, SVD and matrix factorisation. More advanced methods such as generalised linear models, neural networks and Bayesian inference using graphical models are also introduced. The course is self-contained in terms of the necessary mathematical tools (mostly probability) and coding techniques. At the end of the course, students will be able to formalise a ML task, choose the appropriate method in order to tackle it while being able to assess its performance, and to implement these algorithms in Python. Independently of the field, skills in Machine Learning and coding are nowadays almost mandatory in many technical careers (academia, engineering, finance, etc.). This course will provide the students with practical skills in Python for Machine Learning. A strong focus well be put on practice through exercises and projects in Python, one of the preferred language in industry.
This is an introductory module on the Lebesgue theory of measure and integral with application to probability. You are expected to know the theory of Riemann integration. Measure in the line and plane, outer measure, measurable sets, Lebesgue measure, non-measurable sets. Sigma-algebras, measures, probability measures, measurable functions, random variables. Simple functions, Lebesgue integration, integration with respect to general measures. Expectation of random variables. Monotone and dominated convergence theorems, and applications. Absolute continuity and singularity, Radon-Nikodym theorem, probability densities. Possible further topics: product spaces, Fubini's theorem.
This module will provide you with the necessary skills and techniques needed to investigate a variety of practical problems in mathematical finance. It is based on C++, the programming language of choice for many practitioners in the finance industry. You will learn about the basic concepts of the procedural part of C++ (inherited from the earlier C language), before being introduced to the fundamental ideas of object-oriented programming. The module is very ‘hands on’, with weekly sessions in the computer laboratory where you can put your theoretical knowledge into practice with a series of interesting and useful assignments.
This module aims to present some advanced probabilistic concepts and demonstrate their application to stochastic modelling of real-world situations. The topics covered include renewal theory, continuous-time Markov processes and Brownian motion. In addition to exposure to proofs and theoretical material, students develop practical skills through a large number of problems and worked examples. A stochastic process is a system evolving in time in a random way. Besides being of fundamental interest to probability theory, stochastic processes have applications in diverse fields such as financial mathematics, operations research and mathematical biology. This module is an introduction to stochastic processes and related probabilistic concepts. The focus is on continuous time stochastic processes, for which time is an element of the real numbers.