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Sticky continuous processes have consistent price systems

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  • Christian Bender
  • Mikko S. Pakkanen
  • Hasanjan Sayit

Abstract

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni [Math. Finance 16(3), 569-582 (2006)].

Suggested Citation

  • Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," Papers 1310.7857, arXiv.org, revised Aug 2014.
    • Handle: RePEc:arx:papers:1310.7857
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    File URL: http://arxiv.org/pdf/1310.7857
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    References listed on IDEAS

    as
    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. repec:dau:papers:123456789/5630 is not listed on IDEAS
    3. Paolo Guasoni, 2006. "No Arbitrage Under Transaction Costs, With Fractional Brownian Motion And Beyond," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 569-582, July.
    4. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
    5. Erhan Bayraktar & Hasanjan Sayit, 2010. "On the stickiness property," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1109-1112.
    6. Attila Herczegh & Vilmos Prokaj & Mikl'os R'asonyi, 2013. "Diversity and no arbitrage," Papers 1301.4173, arXiv.org, revised Aug 2014.
    7. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    8. repec:crs:wpaper:9513 is not listed on IDEAS
    9. Mikko S. Pakkanen, 2011. "Brownian Semistationary Processes And Conditional Full Support," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 579-586.
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    Cited by:

    1. Sebastian E. Ferrando & Alfredo L. Gonzalez & Ivan L. Degano & Massoome Rahsepar, 2014. "Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals," Papers 1407.1769, arXiv.org, revised Nov 2015.

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