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MA435 Half Unit

Machine Learning in Financial Mathematics

**This information is for the 2022/23 session.**

**Teacher responsible**

Dr Christoph Czichowsky COL 3.11 and Prof Mihail Zervos COL 4.02

**Availability**

This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics, MSc in Quantitative Methods for Risk Management, MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (LSE and Fudan) and MSc in Statistics (Financial Statistics) (Research). This course is not available as an outside option.

**Pre-requisites**

Students must have completed Stochastic Processes (ST409).

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.

**Course content**

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.

**Teaching**

20 hours of lectures, 10 hours of seminars and 5 hours of seminars in the LT.

This course is delivered through a combination of seminars and lectures totalling to 35 hours across Lent Term.

**Formative coursework**

Students will be expected to produce 1 problem sets in the Week 6.

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 (coursework and exam). Students will be expected to submit one piece of formative coursework in the middle of term, on which they will get detailed feedback.

**Indicative reading**

- 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.

**Assessment**

Exam (80%, duration: 2 hours) in the summer exam period.

Coursework (20%) in the LT Week 9.

Written exam (80%) in Summer examination period and coursework (20%) in Lent term. The assessed coursework will be given to the students in Week 7 for submission in Week 9. The coursework consists of a 4 to 5 pages PDF of a Jupyter Notebook (excluding code and pictures that will be given in an appendix). A Jupyter Notebook is a browser-based document containing an ordered list of input/output cells which can contain Python code, text (using Markdown), mathematics, plots and rich media.

** Key facts **

Department: Mathematics

Total students 2021/22: Unavailable

Average class size 2021/22: Unavailable

Controlled access 2021/22: No

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills