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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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    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. Luenberger, David G., 1998. "Products of trees for investment analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1403-1417, August.
    3. repec:dau:papers:123456789/5630 is not listed on IDEAS
    4. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short‐Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232, July.
    5. Jirô Akahori, 2005. "A discrete Itô calculus approach to He’s framework for multi-factor discrete markets," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(3), pages 273-287, September.
    6. 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.
    7. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    8. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-546.
    9. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    10. repec:dau:papers:123456789/1533 is not listed on IDEAS
    11. repec:dau:papers:123456789/5647 is not listed on IDEAS
    12. Tiziano Vargiolu & Silvia Romagnoli, 2000. "Robustness of the Black-Scholes approach in the case of options on several assets," Finance and Stochastics, Springer, vol. 4(3), pages 325-341.
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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. 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.
    3. Yan Dolinsky & Jonathan Zouari, 2017. "Market Delay and G-expectations," Papers 1709.09442, arXiv.org, revised Dec 2018.
    4. 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).
    5. Tomoyuki Ichiba & Seyyed Mostafa Mousavi, 2017. "Option Pricing with Delayed Information," Papers 1707.01600, arXiv.org.
    6. Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.

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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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