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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 coincide 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, 2015. "Super-replication in Fully Incomplete Markets," Papers 1508.05233, arXiv.org, revised Sep 2016.
    • Handle: RePEc:arx:papers:1508.05233
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    References listed on IDEAS

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    1. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    2. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    3. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    4. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    5. 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.
    6. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
    7. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org, revised Oct 2019.
    2. Anna Aksamit & Ivan Guo & Shidan Liu & Zhou Zhou, 2021. "Superhedging duality for multi-action options under model uncertainty with information delay," Papers 2111.14502, arXiv.org, revised Nov 2023.
    3. Ariel Neufeld, 2017. "Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims," Papers 1707.01178, arXiv.org, revised Oct 2018.

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