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The scaling limit of superreplication prices with small transaction costs in the multivariate case

Author

Listed:
  • Peter Bank

    (TU Berlin)

  • Yan Dolinsky

    (Hebrew University)

  • Ari-Pekka Perkkiö

    (TU Berlin)

Abstract

Kusuoka (Ann. Appl. Probab. 5:198–221, 1995) showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset which is traded at properly scaled proportional transaction costs. This article extends the result to a multivariate setup where the investor can trade in several risky assets. The G $G$ -expectation describing the limiting price involves models with a volatility range around the frictionless scaling limit that depends not only on the transaction costs coefficients, but also on the chosen complete discrete-time reference model.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:2:d:10.1007_s00780-016-0320-4
    DOI: 10.1007/s00780-016-0320-4
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Julien Grépat & Yuri Kabanov, 2021. "On a multi-asset version of the Kusuoka limit theorem of option superreplication under transaction costs," Finance and Stochastics, Springer, vol. 25(1), pages 167-187, January.
    2. Tomoyuki Ichiba & Seyyed Mostafa Mousavi, 2017. "Option Pricing with Delayed Information," Papers 1707.01600, arXiv.org.
    3. Dolinsky, Yan & Zouari, Jonathan, 2021. "The value of insider information for super-replication with quadratic transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 394-416.
    4. Yan Dolinsky & Jonathan Zouari, 2017. "Market Delay and G-expectations," Papers 1709.09442, arXiv.org, revised Dec 2018.
    5. Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.
    6. Lin, Zhongguo & Han, Liyan & Li, Wei, 2021. "Option replication with transaction cost under Knightian uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).

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    More about this item

    Keywords

    Superreplication; Transaction costs; Complete model; Limit theorems;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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