Mini-course on adjoints and modern sequence models in finance

Instructors: Prof. Mike Giles (morning); Dr Hans Buehler, Prof. Blanka Horwath, Prof. Mikko Pakkanen, Dr Ben Walker (afternoon)

For details see: https://iccf26.web.ox.ac.uk/speakers-and-program

The first part of this mini-coure gives an introduction to the use of adjoints in computational finance. AAD (Adjoint Algorithmic Differentiation, or sometimes Adjoint Automatic Differentiation) is used extensively in computational finance for estimating sensitivities (Greeks), especially when estimating the sensitivity of a single option value to changes in a large number of input parameters (such as future interest rates or correlation coefficients). The mathematics is also the same as back-propagation in machine learning, computing the sensitivity of the average mis-match to training data to changes in all of the neural network coefficients. The second part offers an accessible introduction to modern sequence models — from the mathematical foundations of transformers and tokenisation through to state space models and neural differential equations — with a particular focus on their emerging role in computational finance. The course is designed for PhD students and researchers with a background in probability, stochastic analysis, or quantitative finance who wish to understand both the theoretical underpinnings and the practical impact of these architectures.