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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
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    References listed on IDEAS

    as
    1. 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.
    2. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic Term Structure Models for SOFR Futures," Papers 2103.11180, arXiv.org.
    3. 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.
    4. 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.
    5. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
    6. 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.
    7. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    8. Christian Bayer & Benjamin Stemper, 2018. "Deep calibration of rough stochastic volatility models," Papers 1810.03399, arXiv.org.
    9. 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.
    10. 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.
    11. 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.
    12. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Heath–Jarrow–Morton framework; Stochastic partial differential equations; Hilbert space neural networks; Forward curves; Futures price; Efficient option pricing; Energy markets;
    All these 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

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