Master the pricing of financial derivatives and their use for hedging financial risks. You study the basics of futures and options, analyse the Black-Scholes and binomial option pricing models, and consider various numerical techniques for pricing financial derivatives. Futures and options are then utilised in the context of hedging financial risks, and you are introduced to the concept of volatility trading and the treatment of volatility as an asset class.

Gain a formal introduction to asset pricing theories and empirical findings. You review the fundamental theories of the expected utility, asset pricing kernels, and risk-neutral valuation, covering the Capital Asset Pricing Model (CAPM), and linear factor models arising from the Arbitrage Pricing Theory (APT). You also discuss empirical asset pricing studies.

Consider the use of modern econometric techniques in the analysis of financial time series. You cover multivariate models for stationary and non-stationary processes, such as Vector Autoregressive models, consider appropriate models for volatility, and study Markov processes and simulation methods used for financial modelling.

Big data - where datasets are so large they cannot be processed using traditional techniques – is useful to financial organisations. This module explores how to analyse big data and covers areas such as predictive analytics, risk modelling and corporate finance. You also learn about the application of data analytics in high frequency finance, fraud and personal finance.

Humans can often perform a task extremely well (e.g., telling cats from dogs) but are unable to understand and describe the decision process followed. Without this explicit knowledge, we cannot write computer programs that can be used by machines to perform the same task. “Machine learning” is the study and application of methods to learn such algorithms automatically from sets of examples, just like babies can learn to tell cats from dogs simply by being shown examples of dogs and cats by their parents. Machine learning has proven particularly suited to cases such as optical character recognition, dictation software, language translators, fraud detection in financial transactions, and many others.

What instruments are used by companies to raise finance and manage financial risk? What is the role of financial institutions operating in financial markets? What are the techniques of financial accounting? How do you use spreadsheets in financial analysis? Examine and develop the concepts and elements of corporate finance.

" Group theory is the study of symmetries, which are actions that preserve structure (such as rotations of the cube). These permeate science at large, playing an important role in physics (particularly particle physics and astrophysics), chemistry (molecules and crystals), cryptography and even music! In this module you will learn advanced constructions and techniques in modern group theory, with special emphasis on the study of finite groups.

In this module you will learn techniques underpinning algorithms for studying integer-valued systems, and apply these algorithms to solve integer and mixed integer problems with cutting-plane algorithms.

The subject of Ordinary Differential Equations (ODEs) is a very important and fascinating branch of mathematics. These equations describe many phenomena, for instance in physics, biology, engineering, chemistry, finance and neuroscience and elsewhere. This module will introduce you to advanced topics in ODEs and dynamical systems.

This module focuses on Bayesian and computational statistics. You will develop your understanding of Bayes’ theorem and Bayesian statistical modelling, and Markov chain Monte Carlo simulation, by developing algorithms for simple probability distributions.

This module will cover partial differential equations (PDEs), which can describe a wide array of physical processes and phenomena. You will learn the properties of first and second order PDEs, the concepts behind them and the methods for solving such equations.

Are you interested in understanding how AlphaGo was able to beat a top Go player? In this module, you will learn about the models behind successful stories of Reinforcement Learning, where a machine (agent) makes sequential decisions to reach an optimal goal. The lectures will be complemented with Lab sessions where we will take advantage of the Open AI Gym environments, allowing us to train our agents to perform tasks such as playing videogames (Atari) and more.