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Calibration of optimal execution of financial transactions in the presence of transient market impact

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  • Enzo Busseti
  • Fabrizio Lillo
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    Abstract

    Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud et al., 2004), which has the property of describing both the volume and the temporal dependence of price change due to trading. We show how this model can be used to describe price impact also in aggregated trade time or in real time. We then solve analytically and calibrate with real data the optimal execution problem both for risk neutral and for risk averse investors and we derive an efficient frontier of optimal execution. When we include spread costs the problem must be solved numerically and we show that the introduction of such costs regularizes the solution.

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    File URL: http://arxiv.org/pdf/1206.0682
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1206.0682.

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    Date of creation: Jun 2012
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    Handle: RePEc:arx:papers:1206.0682

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    1. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
    2. Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
    3. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2004. "Random walks, liquidity molasses and critical response in financial markets," Science & Finance (CFM) working paper archive 500063, Science & Finance, Capital Fund Management.
    4. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
    5. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    6. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    7. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    8. Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico & Loris, Ignace, 2008. "Sparse and stable Markowitz portfolios," Working Paper Series 0936, European Central Bank.
    9. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-46, June.
    10. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
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    Cited by:
    1. 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 May 2014.

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