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Towards Data-Driven Volatility Modeling with Variational Autoencoders

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Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1753))

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Abstract

In this study, we show how S &P 500 Index volatility surfaces can be modeled in a purely data-driven way using variational autoencoders. The approach autonomously learns concepts such as the volatility level, smile, and term structure without leaning on hypotheses from traditional volatility modeling techniques. In addition to introducing notable improvements to an existing variational autoencoder approach for the reconstruction of both complete and incomplete volatility surfaces, we showcase three practical use cases to highlight the relevance of this approach to the financial industry. First, we show how the latent space learned by the variational autoencoder can be used to produce synthetic yet realistic volatility surfaces. Second, we demonstrate how entire sequences of synthetic volatility surfaces can be generated to stress test and analyze an options portfolio. Third and last, we detect anomalous surfaces in our options dataset and pinpoint exactly which subareas are divergent.

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References

  1. Abadi, M., et al.: Tensorflow: a system for large-scale machine learning. In: 12th \(\{\)USENIX\(\}\) Symposium on Operating Systems Design and Implementation (\(\{\)OSDI\(\}\) 16), pp. 265–283 (2016)

    Google Scholar 

  2. Ackerer, D., Tagasovska, N., Vatter, T.: Deep smoothing of the implied volatility surface. Tech. rep., arXiv.org (2020)

    Google Scholar 

  3. Bergeron, M., Fung, N., Hull, J., Poulos, Z.: Variational Autoencoders: a hands-off approach to volatility. arXiv.org:2102.03945 (2021)

  4. Chataigner, M., Crépey, S., Dixon, M.: Deep local volatility. Risks 8(3) (2020). https://doi.org/10.3390/risks8030082

  5. Chen, T., Guestrin, C.: XGBoost: A scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 785–794. KDD ’16, ACM, New York, NY, USA (2016). https://doi.org/10.1145/2939672.2939785

  6. Davis, J., Devos, L., Reyners, S., Schoutens, W.: Gradient boosting for quantitative finance. J. Comput. Finance 24(4), 1–40 (2021). https://doi.org/10.21314/JCF.2020.403

  7. Dupire, B.: Pricing with a smile. Risk Magazine, pp. 18–20 (1994)

    Google Scholar 

  8. Gatheral, J., Jacquier, A.: Arbitrage-free SVI volatility surfaces. Quant. Finance 14(1), 59–71 (2014). https://doi.org/10.1080/14697688.2013.819986

    Article  MATH  Google Scholar 

  9. Heston, S.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Finan. Stud. 6, 327–343 (1993)

    Article  MATH  Google Scholar 

  10. Kingma, D.P., Welling, M.: Auto-encoding variational bayes (2013). https://doi.org/10.48550/ARXIV.1312.6114

  11. Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951). https://doi.org/10.1214/aoms/1177729694

    Article  MATH  Google Scholar 

  12. Lucas, J., Tucker, G., Grosse, R.B., Norouzi, M.: Don’t blame the ELBO! a linear VAE perspective on posterior collapse. In: NeurIPS (2019)

    Google Scholar 

  13. Madan, D., Carr, P., Stanley, M., Chang, E.: The variance gamma process and option pricing. Rev. Finance 2 (1999). https://doi.org/10.1023/A:1009703431535

  14. Nielsen, D., Jaini, P., Hoogeboom, E., Winther, O., Welling, M.: Survae flows: surjections to bridge the gap between VAEs and flows. In: NeurIPS (2020)

    Google Scholar 

  15. Rezende, D.J., Mohamed, S.: Variational inference with normalizing flows. In: Proceedings of the 32nd International Conference on International Conference on Machine Learning - Volume 37, pp. 1530–1538. ICML’15, JMLR.org (2015)

    Google Scholar 

  16. Sohn, K., Lee, H., Yan, X.: Learning structured output representation using deep conditional generative models. In: NIPS (2015)

    Google Scholar 

  17. Wales, D., Doye, J.: Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. The Journal of Physical Chemistry A 101 (1998). https://doi.org/10.1021/jp970984n

  18. Zhu, C., Byrd, R.H., Lu, P., Nocedal, J.: Algorithm 778: L-BFGS-B: fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw. 23(4), 550–560 (1997). https://doi.org/10.1145/279232.279236

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics and Risk, KU Leuven, Leuven, Belgium

    Thomas Dierckx & Wim Schoutens

  2. Department of Computer Science, KU Leuven, Leuven, Belgium

    Thomas Dierckx & Jesse Davis

Authors
  1. Thomas Dierckx
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  2. Jesse Davis
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  3. Wim Schoutens
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Corresponding author

Correspondence to Thomas Dierckx .

Editor information

Editors and Affiliations

  1. University of Sydney, Sydney, Australia

    Irena Koprinska

  2. University of Bari Aldo Moro, Bari, Italy

    Paolo Mignone

  3. University of Pisa, Pisa, Italy

    Riccardo Guidotti

  4. Warsaw University of Technology, Warsaw, Poland

    Szymon Jaroszewicz

  5. Heidelberg University, Heidelberg, Germany

    Holger Fröning

  6. UniCredit, Rome, Italy

    Francesco Gullo

  7. University of Lisbon, Lisbon, Portugal

    Pedro M. Ferreira

  8. Roche, Basel, Switzerland

    Damian Roqueiro

  9. Barcelona Supercomputing Center, Barcelona, Spain

    Gaia Ceddia

  10. Halmstad University, Halmstad, Sweden

    Slawomir Nowaczyk

  11. University of Porto, Porto, Portugal

    João Gama

  12. University of Porto, Porto, Portugal

    Rita Ribeiro

  13. UPC BarcelonaTech, Barcelona, Spain

    Ricard Gavaldà

  14. University of Naples Federico II, Naples, Italy

    Elio Masciari

  15. University of North Carolina, Charlotte, USA

    Zbigniew Ras

  16. ICAR-CNR, Rende, Italy

    Ettore Ritacco

  17. University of Pisa, Pisa, Italy

    Francesca Naretto

  18. Aalen University of Applied Sciences, Aalen, Germany

    Andreas Theissler

  19. Warsaw University of Technology, Warszaw, Poland

    Przemyslaw Biecek

  20. KU Leuven, Leuven, Belgium

    Wouter Verbeke

  21. University of Duisburg-Essen, Essen, Germany

    Gregor Schiele

  22. Graz University of Technology, Graz, Austria

    Franz Pernkopf

  23. AMD, Dublin, Ireland

    Michaela Blott

  24. UniCredit, Rome, Italy

    Ilaria Bordino

  25. UniCredit, Milan, Italy

    Ivan Luciano Danesi

  26. National Agency for New Technologies, Rome, Italy

    Giovanni Ponti

  27. Unicredit, Rome, Italy

    Lorenzo Severini

  28. University of Bari Aldo Moro, Bari, Italy

    Annalisa Appice

  29. University of Bari Aldo Moro, Bari, Italy

    Giuseppina Andresini

  30. University of Lisbon, Lisbon, Portugal

    Ibéria Medeiros

  31. University of Lisbon, Lisbon, Portugal

    Guilherme Graça

  32. Northwestern University, Chicago, USA

    Lee Cooper

  33. Roche, Basel, Switzerland

    Naghmeh Ghazaleh

  34. University of Lausanne, Lausanne, Switzerland

    Jonas Richiardi

  35. Novartis, Basel, Switzerland

    Diego Saldana

  36. Novartis, Basel, Switzerland

    Konstantinos Sechidis

  37. Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy

    Arif Canakoglu

  38. Politecnico di Milano, Milan, Italy

    Sara Pido

  39. Politecnico di Milano, Milan, Italy

    Pietro Pinoli

  40. University of Waikato, Hamilton, New Zealand

    Albert Bifet

  41. Halmstad University, Halmstad, Sweden

    Sepideh Pashami

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Dierckx, T., Davis, J., Schoutens, W. (2023). Towards Data-Driven Volatility Modeling with Variational Autoencoders. In: Koprinska, I., et al. Machine Learning and Principles and Practice of Knowledge Discovery in Databases. ECML PKDD 2022. Communications in Computer and Information Science, vol 1753. Springer, Cham. https://doi.org/10.1007/978-3-031-23633-4_8

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  • DOI: https://doi.org/10.1007/978-3-031-23633-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23632-7

  • Online ISBN: 978-3-031-23633-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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