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Super†replication in fully incomplete markets

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  • Yan Dolinsky
  • Ariel Neufeld

Abstract

In this work, we introduce the notion of fully incomplete markets. We prove that for these markets, the super†replication price coincides with the model†free super†replication price. Namely, the knowledge of the model does not reduce the super†replication price. We provide two families of fully incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples. Our approach is purely probabilistic.

Suggested Citation

  • Yan Dolinsky & Ariel Neufeld, 2018. "Super†replication in fully incomplete markets," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 483-515, April.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:2:p:483-515
    DOI: 10.1111/mafi.12149
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    Cited by:

    1. Ariel Neufeld, 2018. "Buy-And-Hold Property For Fully Incomplete Markets When Super-Replicating Markovian Claims," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-12, December.
    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. Friedrich Hubalek & Walter Schachermayer, 2021. "Convergence of optimal expected utility for a sequence of binomial models," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1315-1331, October.
    4. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.
    5. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2020. "Model-free bounds for multi-asset options using option-implied information and their exact computation," Papers 2006.14288, arXiv.org, revised Jan 2022.

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