Loveless, Benjamin;
(2025)
Z-transform and machine learning techniques for the pricing of discretely monitored path-dependent options.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
This thesis focuses on optimising exotic option pricing using integral and discrete transforms, with a primary emphasis on discrete monitoring of the option. It also explores the broader application of discrete transforms to general problems encountered in physics and signal processing. Numerous methods for computing the inverse $z$-transform are compared to find an alternative to the more popular methods seen in financial applications. Popular modern techniques have an inherent error floor that cannot be improved; thus, a new approach is required and developed in this work. Furthermore, series acceleration is explored to improve CPU times, where the concern is not just raw processing time, but also CPU versus error performance. Pricing algorithms for double barrier and $\alpha$-quantile are presented, utilising a new methodology that focuses on the inverse $z$-transform to achieve a machine-accurate solution. This error level was previously unachievable due to the aforementioned error floor. Series acceleration techniques are further extended to enhance method performance. It can also be demonstrated that the pricing methodology is exponentially convergent in the case of $\alpha$-quantile options, a result previously unverified. Finally, a new approach is presented that utilises deep learning techniques to learn from synthetic data generated by numerical models and predict option prices, as well as the Greeks. An optimised method for parameter searching is also presented. The process offers high performance and is a viable alternative, particularly in scenarios with multiple monitoring dates or multiple repricing events.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Z-transform and machine learning techniques for the pricing of discretely monitored path-dependent options |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2025. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10211946 |
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