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Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims

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  • Ariel Neufeld

Abstract

We show that when the price process $S$ represents a fully incomplete market, the optimal super-replication of any Markovian claim $g(S_T)$ with $g(\cdot)$ being nonnegative and lower semicontinuous is of buy-and-hold type. Since both (unbounded) stochastic volatility models and rough volatility models are examples of fully incomplete markets, one can interpret the buy-and-hold property when super-replicating Markovian claims as a natural phenomenon in incomplete markets.

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  • Ariel Neufeld, 2017. "Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims," Papers 1707.01178, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1707.01178
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    References listed on IDEAS

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    6. Daniel Bartl & Michael Kupper & David J. Promel & Ludovic Tangpi, 2017. "Duality for pathwise superhedging in continuous time," Papers 1705.02933, arXiv.org, revised Apr 2019.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    10. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
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    Citations

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    Cited by:

    1. 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.
    2. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    3. Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.
    4. Yannick Limmer & Blanka Horvath, 2023. "Robust Hedging GANs," Papers 2307.02310, arXiv.org.
    5. Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    6. 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.
    7. Erhan Bayraktar & Yan Dolinsky & Jia Guo, 2018. "Continuity of Utility Maximization under Weak Convergence," Papers 1811.01420, arXiv.org, revised Jun 2020.
    8. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org, revised Oct 2019.
    9. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.

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