Mathematics and Finance

Become familiar with option pricing theory and its mathematical and conceptual underpinnings

Understand the new regulations imposed on banks to require more statistical knowledge and assess the current needs of the financial sector.

Explore probability theory, measure theory and the basic tools from stochastic analysis that provide the mathematical foundations for option pricing theory.

Learn why proper risk management is of utmost importance for the solvency of financial institutions and stability of the entire financial system.

Understand the theory and practice of term structure of interest rates in relation to credit risk, funding liquidity costs, collateral modelling and multiple curves.

Become familiar with programming in C++ and in Python for quantitative finance problems.

Evaluate derivatives used in today’s financial markets and examine simulation methods used in finance and probabilistic numerical methods for PDEs.

Discover how to solve several classes of optimisation problems, including linear, quadratic, stochastic, conic, and robust programming.

Learn the structure and components of multi-layer neural nets and develop deep neural networks to solve computational and statistical problems in finance.

Understand the principles of quantitative portfolio management and apply and implement widely-used approaches such as factor models and momentum strategies.

Discover how quantum computing technology and algorithms can be used to solve financial problems, including portfolio optimisation and data generation.

Develop your understanding of data analysis and ‘machine learning’ techniques, illustrated by applications in finance.

Study specificities of automated trading and develop the mathematical tools required to construct trading algorithms in a high-frequency framework.

Explore the main numerical tools required to work in a quantitative field, including the mathematical techniques underlying Finite difference schemes, Fourier transforms, and quadrature and linear programming.

Develop a thorough understanding of how trades occur in financial markets and learn how to measure liquidity and recognise the recent increase in liquidity fragmentation and hidden, “dark” liquidity.

Apply the main concepts and techniques from dynamics stochastic optimisation and stochastic control theory to the realm of quantitative finance.

Advance your knowledge of derivatives pricing and asset allocation and build familiarity with the stochastic volatility model and jump diffusion model.

Complement your existing financial knowledge by building an appreciation of the specificities of foreign exchange and fixed income markets.

You will explore leading generative AI methods, including denoising diffusion models, flow matching, and neural stochastic differential equations, and discover how these differential equation–based techniques drive cutting-edge image, audio, and video generation (e.g., Stable Diffusion 3, Movie Gen Video) as well as breakthroughs in science such as AlphaFold 3.