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No-dynamic-arbitrage and market impact

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  • Jim Gatheral
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    Abstract

    Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widely assumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that, empirically, these inequalities are typically close to being equalities.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680903373692
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 10 (2010)
    Issue (Month): 7 ()
    Pages: 749-759

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    Handle: RePEc:taf:quantf:v:10:y:2010:i:7:p:749-759

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    Web page: http://www.tandfonline.com/RQUF20

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    Related research

    Keywords: Stochastic volatility; Volatility modelling; Volatility smile fitting; Volatility surfaces; Stochastic jumps; Options volatility; Options pricing;

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    Citations

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    Cited by:
    1. Nico Achtsis & Dirk Nuyens, 2013. "A Monte Carlo method for optimal portfolio executions," Papers 1312.5919, arXiv.org.
    2. E. Bacry & J. F Muzy, 2013. "Hawkes model for price and trades high-frequency dynamics," Papers 1301.1135, arXiv.org.
    3. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2013. "Simulating and analyzing order book data: The queue-reactive model," Papers 1312.0563, arXiv.org.
    4. Olivier Gu\'eant, 2013. "Permanent market impact can be nonlinear," Papers 1305.0413, arXiv.org, revised Mar 2014.
    5. Aur\'elien Alfonsi & Jos\'e Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Papers 1204.2736, arXiv.org.
    6. Olivier Gu\'eant, 2012. "Execution and block trade pricing with optimal constant rate of participation," Papers 1210.7608, arXiv.org, revised Dec 2013.
    7. Aurélien Alfonsi & José Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Working Papers hal-00687193, HAL.
    8. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.
    9. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    10. Rossella Agliardi & Ramazan Gençay, 2012. "Hedging through a Limit Order Book with Varying Liquidity," Working Paper Series 12_12, The Rimini Centre for Economic Analysis.
    11. Antje Fruth & Torsten Schoeneborn & Mikhail Urusov, 2011. "Optimal trade execution and price manipulation in order books with time-varying liquidity," Papers 1109.2631, arXiv.org.
    12. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.
    13. Takashi Kato, 2011. "An Optimal Execution Problem in Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised May 2012.
    14. Olivier Gu\'eant, 2012. "Optimal execution and block trade pricing: a general framework," Papers 1210.6372, arXiv.org, revised Jul 2013.
    15. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592, arXiv.org.
    16. Hans F\"ollmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    17. Aim\'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Papers 1305.6323, arXiv.org, revised Mar 2014.
    18. Aur\'elien Alfonsi & Alexander Schied & Florian Kl\"ock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Oct 2013.
    19. Víctor de Miguel & Xiaoling Mei & Francisco J. Nogales, 2013. "Multiperiod portfolio selection with transaction and market-impact costs," Statistics and Econometrics Working Papers ws131615, Universidad Carlos III, Departamento de Estadística y Econometría.
    20. Florian Kl\"ock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Papers 1205.4008, arXiv.org, revised Jan 2014.
    21. Alexander Schied & Tao Zhang, 2013. "A hot-potato game under transient price impact and some effects of a transaction tax," Papers 1305.4013, arXiv.org, revised Sep 2013.

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