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Bounds On Multi-Asset Derivatives Via Neural Networks

Author

Listed:
  • LUCA DE GENNARO AQUINO

    (Grenoble Ecole de Management, Department of Accounting, Law and Finance, 12 Rue Pierre Sémard, F-38000 Grenoble, France)

  • CAROLE BERNARD

    (Grenoble Ecole de Management, Department of Accounting, Law and Finance, 12 Rue Pierre Sémard, F-38000 Grenoble, France†Department of Economics and Political Sciences, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium)

Abstract

Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the prices of other similar options, such as spread options and/or basket options on subindices. We show that, in most cases, adding further constraints gives rise to bounds that are considerably tighter. Our approach follows the literature on constrained optimal transport and, in particular, builds on the work of Eckstein & Kupper (2018) [Computation of optimal transport and related hedging problems via penalization and neural networks, Appl. Math. Optimiz. 1–29].

Suggested Citation

  • Luca De Gennaro Aquino & Carole Bernard, 2020. "Bounds On Multi-Asset Derivatives Via Neural Networks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(08), pages 1-31, December.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:08:n:s0219024920500508
    DOI: 10.1142/S0219024920500508
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    Citations

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    Cited by:

    1. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    2. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    3. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.
    4. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    5. Evangelia Dragazi & Shuaiqiang Liu & Antonis Papapantoleon, 2024. "Improved model-free bounds for multi-asset options using option-implied information and deep learning," Papers 2404.02343, arXiv.org.
    6. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    7. Ariel Neufeld & Julian Sester, 2021. "A deep learning approach to data-driven model-free pricing and to martingale optimal transport," Papers 2103.11435, arXiv.org, revised Dec 2022.

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