Mixture of Normalizing Flows for European Option Pricing

Yongxin Yang, Timothy M. Hospedales
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:2390-2399, 2023.

Abstract

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 \url{https://github.com/qmfin/MoNF}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-yang23b, title = {Mixture of Normalizing Flows for {E}uropean Option Pricing}, author = {Yang, Yongxin and Hospedales, Timothy M.}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {2390--2399}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/yang23b/yang23b.pdf}, url = {https://proceedings.mlr.press/v216/yang23b.html}, abstract = {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 \url{https://github.com/qmfin/MoNF}.} }
Endnote
%0 Conference Paper %T Mixture of Normalizing Flows for European Option Pricing %A Yongxin Yang %A Timothy M. Hospedales %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-yang23b %I PMLR %P 2390--2399 %U https://proceedings.mlr.press/v216/yang23b.html %V 216 %X 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 \url{https://github.com/qmfin/MoNF}.
APA
Yang, Y. & Hospedales, T.M.. (2023). Mixture of Normalizing Flows for European Option Pricing. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:2390-2399 Available from https://proceedings.mlr.press/v216/yang23b.html.

Related Material