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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

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.

Suggested Citation

  • Enzo Busseti & Fabrizio Lillo, 2012. "Calibration of optimal execution of financial transactions in the presence of transient market impact," Papers 1206.0682, arXiv.org.
    • Handle: RePEc:arx:papers:1206.0682
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    References listed on IDEAS

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    1. Giannone, Domenico & De Mol, Christine & Daubechies, Ingrid & Brodie, Joshua, 2007. "Sparse and Stable Markowitz Portfolios," CEPR Discussion Papers 6474, C.E.P.R. Discussion Papers.
    2. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    3. Lee, Charles M C & Ready, Mark J, 1991. "Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-746, June.
    4. 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.
    5. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    6. 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.
    7. 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.
    8. 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.
    9. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    10. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2003. "Master curve for price-impact function," Nature, Nature, vol. 421(6919), pages 129-130, January.
    11. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    12. 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.
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    Cited by:

    1. Fengpei Li & Vitalii Ihnatiuk & Ryan Kinnear & Anderson Schneider & Yuriy Nevmyvaka, 2022. "Do price trajectory data increase the efficiency of market impact estimation?," Papers 2205.13423, arXiv.org, revised Mar 2023.
    2. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2014. "Optimal execution with nonlinear transient market impact," Papers 1412.4839, arXiv.org.
    3. Aur'elien Alfonsi & Alexander Schied & Florian Klock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Sep 2015.
    4. Alexander Barzykin & Fabrizio Lillo, 2019. "Optimal VWAP execution under transient price impact," Papers 1901.02327, arXiv.org, revised Jan 2019.
    5. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2017. "Optimal execution with non-linear transient market impact," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 41-54, January.
    6. Aurélien Alfonsi & Florian Klöck & Alexander Schied, 2016. "Multivariate Transient Price Impact and Matrix-Valued Positive Definite Functions," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 914-934, August.
    7. Johannes Muhle‐Karbe & Zexin Wang & Kevin Webster, 2023. "A Leland model for delta hedging in central risk books," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 504-547, July.
    8. Dirk Becherer & Todor Bilarev, 2018. "Hedging with physical or cash settlement under transient multiplicative price impact," Papers 1807.05917, arXiv.org, revised Jun 2023.

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