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Optimal multifactor trading under proportional transaction costs

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  • Richard J. Martin

Abstract

Proportional transaction costs present difficult theoretical problems in trading algorithm design, on account of their lack of analytical tractability. The author derives a solution of DT-NT-DT form for an arbitrary model in which the the traded asset has diffusive dynamics described by one or more stochastic risk factors. The width of the NT zone is found to be, as expected, proportional to the cube root of the transaction cost. It is also proportional to the 2/3 power of the volatility of the target position, thereby causing a faster trading strategy to be buffered more than a slower one. The displacement of the middle of the buffer from the costfree position is found to be proportional to the square of the width, and hence to the 2/3 power of the transaction cost; the proportionality constant depends on the expected short-term change in position.

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  • Richard J. Martin, 2012. "Optimal multifactor trading under proportional transaction costs," Papers 1204.6488, arXiv.org.
    • Handle: RePEc:arx:papers:1204.6488
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    References listed on IDEAS

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    1. Nicolae Gârleanu & Lasse Heje Pedersen, 2013. "Dynamic Trading with Predictable Returns and Transaction Costs," Journal of Finance, American Finance Association, vol. 68(6), pages 2309-2340, December.
    2. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    3. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324, July.
    4. Joachim de Lataillade & Cyril Deremble & Marc Potters & Jean-Philippe Bouchaud, 2012. "Optimal Trading with Linear Costs," Papers 1203.5957, arXiv.org.
    5. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    6. Richard Martin & Torsten Schoneborn, 2011. "Mean Reversion Pays, but Costs," Papers 1103.4934, arXiv.org.
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    Citations

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    Cited by:

    1. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org, revised Mar 2015.
    2. Richard J Martin, 2016. "Universal trading under proportional transaction costs," Papers 1603.06558, arXiv.org.
    3. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2013. "Some applications of first-passage ideas to finance," Papers 1306.3110, arXiv.org.
    4. Joachim de Lataillade & Ayman Chaouki, 2020. "Equations and Shape of the Optimal Band Strategy," Papers 2003.04646, arXiv.org, revised Mar 2020.
    5. Florian Krach & Josef Teichmann & Hanna Wutte, 2024. "Robust Utility Optimization via a GAN Approach," Papers 2403.15243, arXiv.org.
    6. Filippo Passerini & Samuel E. Vazquez, 2015. "Optimal Trading with Alpha Predictors," Papers 1501.03756, arXiv.org, revised Jan 2015.
    7. Richard J. Martin, 2021. "Design and analysis of momentum trading strategies," Papers 2101.01006, arXiv.org, revised Jan 2023.
    8. Christoph Kuhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision," Papers 1309.5235, arXiv.org, revised Feb 2015.
    9. Joachim de Lataillade & Cyril Deremble & Marc Potters & Jean-Philippe Bouchaud, 2012. "Optimal Trading with Linear Costs," Papers 1203.5957, arXiv.org.
    10. Kühn, Christoph & Muhle-Karbe, Johannes, 2015. "Optimal liquidity provision," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2493-2515.
    11. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    12. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    13. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    14. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    15. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.

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