IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v28y2024i1d10.1007_s00780-023-00520-2.html
   My bibliography  Save this article

Pricing options on flow forwards by neural networks in a Hilbert space

Author

Listed:
  • Fred Espen Benth

    (University of Oslo)

  • Nils Detering

    (University of California at Santa Barbara)

  • Luca Galimberti

    (King’s College London)

Abstract

We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimisation problem in a Hilbert space of real-valued functions on the positive real line, which is the state space for the term structure dynamics. This optimisation problem is solved by using a feedforward neural network architecture designed for approximating continuous functions on the state space. The proposed neural network is built upon the basis of the Hilbert space. We provide case studies that show its numerical efficiency, with superior performance over that of a classical neural network trained on sampling the term structure curves.

Suggested Citation

  • Fred Espen Benth & Nils Detering & Luca Galimberti, 2024. "Pricing options on flow forwards by neural networks in a Hilbert space," Finance and Stochastics, Springer, vol. 28(1), pages 81-121, January.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:1:d:10.1007_s00780-023-00520-2
    DOI: 10.1007/s00780-023-00520-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-023-00520-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-023-00520-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models," Finance and Stochastics, Springer, vol. 25(4), pages 615-657, October.
    2. Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse & Tuan Anh Nguyen, 2020. "A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations," Partial Differential Equations and Applications, Springer, vol. 1(2), pages 1-34, April.
    3. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential L\'evy models," Papers 2101.11897, arXiv.org, revised Jul 2021.
    4. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    5. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic Term Structure Models for SOFR Futures," Papers 2103.11180, arXiv.org.
    6. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic term structure models for SOFR futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1520-1544, October.
    7. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2021. "Accuracy of deep learning in calibrating HJM forward curves," Digital Finance, Springer, vol. 3(3), pages 209-248, December.
    8. Christian Bayer & Benjamin Stemper, 2018. "Deep calibration of rough stochastic volatility models," Papers 1810.03399, arXiv.org.
    9. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    10. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, February.
    11. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2020. "Accuracy of Deep Learning in Calibrating HJM Forward Curves," Papers 2006.01911, arXiv.org, revised May 2021.
    12. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
    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. Fred Espen Benth & Nils Detering & Luca Galimberti, 2022. "Pricing options on flow forwards by neural networks in Hilbert space," Papers 2202.11606, arXiv.org.
    2. Lukas Gonon, 2024. "Deep neural network expressivity for optimal stopping problems," Finance and Stochastics, Springer, vol. 28(3), pages 865-910, July.
    3. Fred Espen Benth & Carlo Sgarra, 2024. "A Barndorff-Nielsen and Shephard model with leverage in Hilbert space for commodity forward markets," Finance and Stochastics, Springer, vol. 28(4), pages 1035-1076, October.
    4. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    5. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2021. "Accuracy of deep learning in calibrating HJM forward curves," Digital Finance, Springer, vol. 3(3), pages 209-248, December.
    6. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2020. "Accuracy of Deep Learning in Calibrating HJM Forward Curves," Papers 2006.01911, arXiv.org, revised May 2021.
    7. Sven Karbach, 2024. "Heat modulated affine stochastic volatility models for forward curve dynamics," Papers 2409.13070, arXiv.org.
    8. Cuchiero, Christa & Di Persio, Luca & Guida, Francesco & Svaluto-Ferro, Sara, 2024. "Measure-valued affine and polynomial diffusions," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    9. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    10. 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.
    11. Brugler, James & Khomyn, Marta & Putniņs̆, Tālis, 2025. "Benchmarking benchmarks," Journal of Financial Economics, Elsevier, vol. 168(C).
    12. Iván Blanco, Juan Ignacio Peña, and Rosa Rodriguez, 2018. "Modelling Electricity Swaps with Stochastic Forward Premium Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    13. Piccirilli, Marco & Schmeck, Maren Diane & Vargiolu, Tiziano, 2021. "Capturing the power options smile by an additive two-factor model for overlapping futures prices," Energy Economics, Elsevier, vol. 95(C).
    14. Benth, Fred Espen & Schroers, Dennis & Veraart, Almut E.D., 2022. "A weak law of large numbers for realised covariation in a Hilbert space setting," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 241-268.
    15. Fang, Dong-Jie & Yeh, Zong-Wei & He, Jie-Cao & Lin, Shih-Kuei, 2024. "What drives jumps in the secured Overnight Financing Rate? Evidence from the arbitrage-free Nelson–Siegel model with jump diffusion," Pacific-Basin Finance Journal, Elsevier, vol. 86(C).
    16. Damiano Brigo & Xiaoshan Huang & Andrea Pallavicini & Haitz Saez de Ocariz Borde, 2021. "Interpretability in deep learning for finance: a case study for the Heston model," Papers 2104.09476, arXiv.org.
    17. Alan Brace & Karol Gellert & Erik Schlögl, 2024. "SOFR term structure dynamics—Discontinuous short rates and stochastic volatility forward rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(6), pages 936-985, June.
    18. Francesca Biagini & Lukas Gonon & Niklas Walter, 2023. "Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models," Papers 2309.14784, arXiv.org.
    19. Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org.
    20. Nils Detering & Silvia Lavagnini, 2025. "A class of locally state-dependent models for forward curves," Papers 2502.09486, arXiv.org, revised Mar 2025.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

    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:spr:finsto:v:28:y:2024:i:1:d:10.1007_s00780-023-00520-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.