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A Note on Utility Indifference Pricing with Delayed Information

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  • Peter Bank
  • Yan Dolinsky

Abstract

We consider the Bachelier model with information delay where investment decisions can be based only on observations from $H>0$ time units before. Utility indifference prices are studied for vanilla options and we compute their non-trivial scaling limit for vanishing delay when risk aversion is scaled liked $A/H$ for some constant $A$. Using techniques from [7], we develop discrete-time duality for this setting and show how the relaxed form of martingale property introduced by [9] results in the scaling limit taking the form of a volatility control problem with quadratic penalty.

Suggested Citation

  • Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2011.05023
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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. Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.
    3. Martin Schweizer & Danijel Zivoi & Mario Sikic, 2017. "Dynamic Mean-Variance Optimisation Problems with Deterministic Information," Swiss Finance Institute Research Paper Series 17-29, Swiss Finance Institute, revised Feb 2018.
    4. Martin Schweizer & Danijel Zivoi & Mario Šikić, 2018. "Dynamic Mean–Variance Optimization Problems With Deterministic Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, March.
    5. Tomoyuki Ichiba & Seyyed Mostafa Mousavi, 2017. "Option Pricing with Delayed Information," Papers 1707.01600, arXiv.org.
    6. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    7. 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.
    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. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    10. 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.
    11. 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. Yan Dolinsky, 2023. "Delayed Semi-static Hedging in the Continuous Time Bachelier Model," Papers 2311.17270, arXiv.org, revised Sep 2024.
    2. Asaf Cohen & Yan Dolinsky, 2022. "A scaling limit for utility indifference prices in the discretised Bachelier model," Finance and Stochastics, Springer, vol. 26(2), pages 335-358, April.
    3. 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.
    4. Asaf Cohen & Yan Dolinsky, 2021. "A Scaling Limit for Utility Indifference Prices in the Discretized Bachelier Model," Papers 2102.11968, arXiv.org, revised Mar 2022.
    5. Yan Dolinsky & Or Zuk, 2023. "Explicit Computations for Delayed Semistatic Hedging," Papers 2308.10550, arXiv.org, revised Sep 2024.
    6. Yan Dolinsky & Or Zuk, 2023. "Exponential Utility Maximization in a Discrete Time Gaussian Framework," Papers 2305.18136, arXiv.org, revised Jun 2023.

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