IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2509.05911.html
   My bibliography  Save this paper

Deep Learning Option Pricing with Market Implied Volatility Surfaces

Author

Listed:
  • Lijie Ding
  • Egang Lu
  • Kin Cheung

Abstract

We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S\&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data for American puts and arithmetic Asian options using QuantLib. To address the high dimensionality of volatility surfaces, we employ a variational autoencoder (VAE) that compresses volatility surfaces across maturities and strikes into a 10-dimensional latent representation. We feed these latent variables, combined with option-specific inputs such as strike and maturity, into a multilayer perceptron to predict option prices. Our model is trained in stages: first to train the VAE for volatility surface compression and reconstruction, then options pricing mapping, and finally fine-tune the entire network end-to-end. The trained pricer achieves high accuracy across American and Asian options, with prediction errors concentrated primarily near long maturities and at-the-money strikes, where absolute bid-ask price differences are known to be large. Our method offers an efficient and scalable approach requiring only a single neural network forward pass and naturally improve with additional data. By bridging volatility surface modeling and option pricing in a unified framework, it provides a fast and flexible alternative to traditional numerical approaches for exotic options.

Suggested Citation

  • Lijie Ding & Egang Lu & Kin Cheung, 2025. "Deep Learning Option Pricing with Market Implied Volatility Surfaces," Papers 2509.05911, arXiv.org.
  • Handle: RePEc:arx:papers:2509.05911
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2509.05911
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
    2. Jing Wang & Shuaiqiang Liu & Cornelis Vuik, 2025. "Controllable Generation of Implied Volatility Surfaces with Variational Autoencoders," Papers 2509.01743, arXiv.org.
    3. Lijie Ding & Egang Lu & Kin Cheung, 2025. "Fast Derivative Valuation from Volatility Surfaces using Machine Learning," Papers 2505.22957, arXiv.org.
    4. Hainaut, Donatien & Casas, Alex, 2024. "Option pricing in the Heston model with Physics inspired neural networks," LIDAM Discussion Papers ISBA 2024002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Donatien Hainaut & Alex Casas, 2024. "Option pricing in the Heston model with physics inspired neural networks," Annals of Finance, Springer, vol. 20(3), pages 353-376, September.
    6. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    7. Xiang Wang & Jessica Li & Jichun Li, 2023. "A Deep Learning Based Numerical PDE Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 149-164, June.
    8. Raquel M. Gaspar & Sara D. Lopes & Bernardo Sequeira, 2020. "Neural Network Pricing of American Put Options," Risks, MDPI, vol. 8(3), pages 1-24, July.
    9. Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
    10. Philip Ndikum, 2020. "Machine Learning Algorithms for Financial Asset Price Forecasting," Papers 2004.01504, arXiv.org.
    11. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Learning for Exotic Option Valuation," Papers 2103.12551, arXiv.org, revised Sep 2021.
    12. Maxime Bergeron & Nicholas Fung & John Hull & Zissis Poulos, 2021. "Variational Autoencoders: A Hands-Off Approach to Volatility," Papers 2102.03945, arXiv.org.
    13. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    15. Ali Hirsa & Tugce Karatas & Amir Oskoui, 2019. "Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes," Papers 1902.05810, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Naman Krishna Pande & Puneet Pasricha & Arun Kumar & Arvind Kumar Gupta, 2024. "European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning," Papers 2410.10474, arXiv.org.
    2. S'andor Kuns'agi-M'at'e & G'abor F'ath & Istv'an Csabai & G'abor Moln'ar-S'aska, 2022. "Deep Weighted Monte Carlo: A hybrid option pricing framework using neural networks," Papers 2208.14038, arXiv.org, revised Dec 2022.
    3. Jaegi Jeon & Kyunghyun Park & Jeonggyu Huh, 2021. "Extensive networks would eliminate the demand for pricing formulas," Papers 2101.09064, arXiv.org.
    4. Shuaiqiang Liu & Anastasia Borovykh & Lech A. Grzelak & Cornelis W. Oosterlee, 2019. "A neural network-based framework for financial model calibration," Papers 1904.10523, arXiv.org.
    5. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.
    6. Andrew Na & Meixin Zhang & Justin Wan, 2023. "Computing Volatility Surfaces using Generative Adversarial Networks with Minimal Arbitrage Violations," Papers 2304.13128, arXiv.org, revised Dec 2023.
    7. Timothy DeLise, 2021. "Neural Options Pricing," Papers 2105.13320, arXiv.org.
    8. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    9. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    10. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
    11. Junike, Gero & Pankrashkin, Konstantin, 2022. "Precise option pricing by the COS method—How to choose the truncation range," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    12. Sangseop Lim & Chang-hee Lee & Won-Ju Lee & Junghwan Choi & Dongho Jung & Younghun Jeon, 2022. "Valuation of the Extension Option in Time Charter Contracts in the LNG Market," Energies, MDPI, vol. 15(18), pages 1-14, September.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    15. Jing Wang & Shuaiqiang Liu & Cornelis Vuik, 2025. "Controllable Generation of Implied Volatility Surfaces with Variational Autoencoders," Papers 2509.01743, arXiv.org.
    16. Daniel Guterding, 2023. "Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities," Risks, MDPI, vol. 11(5), pages 1-24, April.
    17. Hyun-Gyoon Kim & Hyeongmi Kim & Jeonggyu Huh, 2025. "Considering Appropriate Input Features of Neural Network to Calibrate Option Pricing Models," Computational Economics, Springer;Society for Computational Economics, vol. 66(1), pages 77-104, July.
    18. Thaddeus Neururer & George Papadakis & Edward J. Riedl, 2016. "Tests of investor learning models using earnings innovations and implied volatilities," Review of Accounting Studies, Springer, vol. 21(2), pages 400-437, June.
    19. Jovanka Lili Matic & Natalie Packham & Wolfgang Karl Härdle, 2023. "Hedging cryptocurrency options," Review of Derivatives Research, Springer, vol. 26(1), pages 91-133, April.
    20. Sarit Maitra & Vivek Mishra & Goutam Kr. Kundu & Kapil Arora, 2023. "Integration of Fractional Order Black-Scholes Merton with Neural Network," Papers 2310.04464, arXiv.org, revised Oct 2023.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2509.05911. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.