Mixture of Normalizing Flows for European Option Pricing

Yongxin Yang, Timothy M Hospedales

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

We present a mixture of normalizing flows (MoNF) approach to European option pricing with guarantees that its estimations are free from static arbitrage. In contrast to many existing methods that meet economic rationality constraints (e.g., non-arbitrage) by introducing auxiliary losses, our solution meets those constraints exactly by design. To achieve this, we propose to build a model for risk neutral density using normalizing flows, which results in a pricing model, instead of modelling the option pricing function directly. First, we convert the constraints for direct pricing models to the constraints for models backed by risk neutral density estimation, then we design a specific NF architecture that meets these constraints. Furthermore, we find that employing a mixture of such normalizing flows improves the performance significantly, compared to using a deeper single NF. Finally, we present a mechanism to regularise the proposed model, and this regularisation can serve as a bridge between our method and any sample-based mathematical finance method. The evaluations on five option datasets show superiority of our method compared to mathematical finance solutions and some other neural networks based methods. The code is available at https://github.com/qmfin/MoNF.
Original languageEnglish
Title of host publicationThe 39th Conference on Uncertainty in Artificial Intelligence
Number of pages10
Publication statusPublished - 2 Jul 2023
Event39th Conference on Uncertainty in Artificial Intelligence - Pittsburgh, United States
Duration: 31 Jul 20234 Aug 2023
Conference number: 39

Publication series

NameProceedings of Machine Learning Research
ISSN (Electronic)2640-3498


Conference39th Conference on Uncertainty in Artificial Intelligence
Abbreviated titleUAI 2023
Country/TerritoryUnited States
Internet address


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