MA435      Half Unit
Machine Learning in Financial Mathematics

This information is for the 2025/26 session.

Course Convenor

Availability

Requisites

Pre-requisites:

Students must have completed ST409 before taking this course.

Additional requisites:

Students are expected to have done ST409; students who haven't done ST409 need to obtain permission from the lecturer by providing a statement explaining why and how they know the material covered in ST409. Students are also expected to have basic Python programming skills and good command of linear algebra and calculus.

This course introduces a range of computational problems in financial markets and illustrates how they can be addressed by using tools from machine learning. In particular, portfolio optimisation, optimal trade execution, pricing and hedging of financial derivatives and calibration of stochastic volatility models are included. The course considers some theoretical results on machine learning basics such as empirical risk minimisation, bias-complexity tradeoff, model selection and validation as well as more advanced topics such as deep learning, feedforward neural networks, universal approximation theorems, stochastic gradient descent, back propagation, regularisation and different neural network architectures. Practical implementation in Python and training of neural networks for the above problems in financial markets are also addressed.

10 hours of seminars and 20 hours of lectures in the Winter Term.

This course is delivered through a combination of seminars and lectures totalling to 30 hours across WT. 

Problem sets

The main formative assessment will be in the form of weekly exercise sets, which will be discussed in the seminars.

Some of the topics of these will be similar to what is expected in the summative assessment (exam).

• M. Dixon, I. Halperin and P. Bilokon. Machine Learning in Finance. Springer, 2020.
• H. Ni, G. Yu, J. Zheng and X. Dong, An Introduction to Machine Learning and Quantitative Finance. World Scientific, 2021.
• C.M. Bishop, Pattern Recognition and Machine Learning. Springer, 2006.
• S. Shalev-Shwartz and S. Ben-David, Understanding Machine Learning. Cambridge University Press, 2014.
• I. Goodfellow, Y. Bengio and A. Courville, Deep Learning. MIT Press, 2016.
• J. M. Hutchinson, A. Lo and T. Poggio, A Nonparametric Approach to Pricing and Hedging Derivatives Securities Via Learning Networks. Journal of Finance , 1994.
• H. Buehler, L. Gonon, J. Teichmann and B. Wood, Deep Hedging. Quantitative Finance, 2019.
• J. Ruf and W. Wang, Hedging with Linear Regressions and Neural Networks. To appear in Journal of Business & Economics Statistics, 2021.
• A. Hernandez, Model Calibration with Neural Networks. Risk, 2017.
• B. Horvath, A. Muruguza and M. Tomas, Deep Learning Volatility: a Deep Learning Network Perspective on Pricing and Calibration in (Rough) Volatility Models. Quantitative Finance, 2021.

Exam (75%), duration: 120 Minutes in the Spring exam period

Project (25%)

This component of assessment includes an element of group work.