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Market delay and G-expectations

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  • Dolinsky, Yan
  • Zouari, Jonathan

Abstract

We study super-replication of contingent claims in markets with delayed filtration. The first result in this paper reveals that in the Black–Scholes model with constant delay the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies. Our second result says that the scaling limit of super-replication prices for binomial models with a fixed number of times of delay H is equal to the G-expectation with volatility uncertainty interval [0,σH+1].

Suggested Citation

  • Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:694-707
    DOI: 10.1016/j.spa.2019.03.007
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    References listed on IDEAS

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    1. Ariel Neufeld, 2017. "Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims," Papers 1707.01178, arXiv.org, revised Oct 2018.
    2. Peter Bank & Yan Dolinsky & Ari-Pekka Perkkiö, 2017. "The scaling limit of superreplication prices with small transaction costs in the multivariate case," Finance and Stochastics, Springer, vol. 21(2), pages 487-508, April.
    3. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
    4. Tomoyuki Ichiba & Seyyed Mostafa Mousavi, 2017. "Option Pricing with Delayed Information," Papers 1707.01600, arXiv.org.
    5. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    6. 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.
    7. Darrell Duffie & Philip Protter, 1992. "From Discrete‐ to Continuous‐Time Finance: Weak Convergence of the Financial Gain Process1," Mathematical Finance, Wiley Blackwell, vol. 2(1), pages 1-15, January.
    8. Ariel Neufeld, 2018. "Buy-And-Hold Property For Fully Incomplete Markets When Super-Replicating Markovian Claims," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-12, December.
    9. Rüdiger Frey, 2000. "Risk Minimization with Incomplete Information in a Model for High‐Frequency Data," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 215-225, April.
    10. Christa Cuchiero & Irene Klein & Josef Teichmann, 2017. "A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting," Papers 1705.02087, arXiv.org.
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    Cited by:

    1. Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    2. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkiö, 2023. "Optional projection under equivalent local martingale measures," Finance and Stochastics, Springer, vol. 27(2), pages 435-465, April.

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