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Optimal multifactor trading under proportional transaction costs

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  • Richard J. Martin
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    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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    File URL: http://arxiv.org/pdf/1204.6488
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1204.6488.

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    Date of creation: Apr 2012
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    Handle: RePEc:arx:papers:1204.6488

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    1. Richard Martin & Torsten Sch\"oneborn, 2011. "Mean Reversion Pays, but Costs," Papers 1103.4934, arXiv.org.
    2. 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.
    3. Garleanu, Nicolae Bogdan & Pedersen, Lasse Heje, 2009. "Dynamic Trading with Predictable Returns and Transaction Costs," CEPR Discussion Papers 7392, C.E.P.R. Discussion Papers.
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    Cited by:
    1. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org.
    2. Ren Liu & Johannes Muhle-Karbe & Marko Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org.
    3. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    4. Christoph K\"uhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision in Limit Order Markets," Papers 1309.5235, arXiv.org, revised May 2014.
    5. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.

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