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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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    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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